#############################################################################
##
#W standard/attributes/inverse.tst
#Y Copyright (C) 2015-2022 Wilf A. Wilson
##
## Licensing information can be found in the README file of this package.
#
#############################################################################
##
#@local D, I, S, T, W, acting, an, elts, es, f, foo, gens, h, iso, jid, n, reps
#@local small, x
gap> START_TEST("Semigroups package: standard/attributes/inverse.tst");
gap> LoadPackage("semigroups", false);;
#
gap> SEMIGROUPS.StartTest();
# attrinv: VagnerPrestonRepresentation, symmetric inv monoid 4 1/1
gap> S := InverseSemigroup([
> PartialPerm([2, 3, 4, 1]),
> PartialPerm([2, 1, 3, 4]),
> PartialPerm([1, 2, 3, 0])]);;
gap> Size(S);
209
gap> Size(S) = Size(SymmetricInverseMonoid(4));
true
gap> iso := VagnerPrestonRepresentation(S);;
gap> DegreeOfPartialPermSemigroup(Range(iso));
209
# attrinv: SameMinorantsSubgroup, symmetric inv monoid 5 1/2
gap> S := SymmetricInverseSemigroup(5);;
gap> h := HClass(S, One(S));
<Green's H-class: <identity partial perm on [ 1, 2, 3, 4, 5 ]>>
gap> SameMinorantsSubgroup(h);
[ <identity partial perm on [ 1, 2, 3, 4, 5 ]> ]
gap> h := HClass(S, PartialPerm([1, 2, 0, 0, 0]));
<Green's H-class: <identity partial perm on [ 1, 2 ]>>
gap> SameMinorantsSubgroup(h);
[ <identity partial perm on [ 1, 2 ]> ]
gap> h := HClass(S, MultiplicativeZero(S));
<Green's H-class: <empty partial perm>>
gap> SameMinorantsSubgroup(h);
[ <empty partial perm> ]
# attrinv: SameMinorantsSubgroup, error 2/2
gap> S := FullTransformationMonoid(5);;
gap> h := HClass(S, One(S));
<Green's H-class: IdentityTransformation>
gap> SameMinorantsSubgroup(h);
Error, the parent of the argument (a group H-class) must be an inverse semigro\
up
# attrinv: Minorants, error, 1
gap> S := SymmetricInverseMonoid(3);;
gap> f := PartialPerm([1, 2, 3, 4]);;
gap> Minorants(S, f);
Error, the 2nd argument (a mult. elt.) is not an element of the 1st argument (\
an inverse semigroup)
gap> f := PartialPerm([1, 2, 3]);;
gap> Set(Minorants(S, f));
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>, <identity partial perm on [ 1, 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 2, 3 ]>,
<identity partial perm on [ 1, 3 ]> ]
gap> NaturalPartialOrder(S);;
gap> Minorants(S, f);
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>, <identity partial perm on [ 1, 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 2, 3 ]>,
<identity partial perm on [ 1, 3 ]> ]
gap> f := PartialPerm([1, 3, 2]);;
# attrinv: Minorants, not idempotent, 2
gap> S := Semigroup([
> PartialPerm([1, 2, 3, 4], [1, 2, 3, 4]),
> PartialPerm([1, 2, 3], [2, 3, 1])]);;
gap> IsInverseSemigroup(S);
true
gap> Minorants(S, GeneratorsOfSemigroup(S)[2]);
[ ]
gap> S := Semigroup(S, rec(acting := false));;
gap> IsInverseSemigroup(S);
true
gap> Minorants(S, GeneratorsOfSemigroup(S)[1]);
[ <identity partial perm on [ 1, 2, 3 ]> ]
# attrinv: character tables of inverse acting semigroups
# Some random examples to test consistency of old code with new
gap> gens := [
> [PartialPerm([1, 2, 3, 4, 6, 8, 9], [1, 5, 3, 8, 9, 4, 10])],
> [PartialPerm([1, 2, 3, 4, 5, 6], [3, 8, 4, 6, 5, 7]),
> PartialPerm([1, 2, 3, 4, 5, 7], [1, 4, 3, 2, 7, 6]),
> PartialPerm([1, 2, 3, 5, 6, 8], [5, 7, 1, 4, 2, 6])],
> [PartialPerm([1, 2, 3, 5], [2, 1, 7, 3]),
> PartialPerm([1, 2, 4, 5, 6], [7, 3, 1, 4, 2]),
> PartialPerm([1, 2, 3, 4, 6], [7, 6, 5, 1, 2]),
> PartialPerm([1, 3, 6, 7], [6, 3, 1, 4])],
> [PartialPerm([1, 2, 3, 5], [1, 6, 4, 7]),
> PartialPerm([1, 2, 3, 6], [1, 6, 5, 2]),
> PartialPerm([1, 2, 3, 5, 6, 7], [4, 3, 5, 7, 1, 6]),
> PartialPerm([1, 2, 3, 4, 7], [6, 4, 2, 3, 1])],
> [PartialPerm([1, 2, 3, 5, 6], [5, 3, 7, 4, 1]),
> PartialPerm([1, 2, 3, 4, 5, 7], [3, 1, 5, 7, 6, 2])],
> [PartialPerm([1, 2, 3, 4, 5, 6, 9], [1, 5, 9, 2, 6, 10, 7]),
> PartialPerm([1, 3, 4, 7, 8, 9], [9, 4, 1, 6, 2, 8]),
> PartialPerm([1, 2, 3, 4, 5, 9], [9, 3, 8, 2, 10, 7])],
> [PartialPerm([1, 2, 3, 4, 5], [6, 4, 1, 2, 7]),
> PartialPerm([1, 2, 3, 6], [3, 5, 7, 4]),
> PartialPerm([1, 2, 3, 4, 5, 6, 7], [1, 7, 9, 5, 2, 8, 4])],
> [PartialPerm([1, 2, 4], [3, 6, 2]),
> PartialPerm([1, 2, 3, 4], [6, 3, 2, 1]),
> PartialPerm([1, 2, 3, 6], [4, 6, 3, 1]),
> PartialPerm([1, 2, 3, 5, 6], [5, 6, 3, 2, 4])],
> [PartialPerm([1, 2, 3, 4], [3, 5, 1, 2]),
> PartialPerm([1, 2, 3, 4], [5, 4, 2, 1]),
> PartialPerm([1, 2, 4, 5], [3, 5, 1, 2])],
> [PartialPerm([1, 2, 3, 5], [4, 1, 2, 3])]];;
gap> S := List(gens, x -> InverseSemigroup(x, rec(acting := true)));
[ <inverse partial perm semigroup of rank 9 with 1 generator>,
<inverse partial perm semigroup of rank 8 with 3 generators>,
<inverse partial perm semigroup of rank 7 with 4 generators>,
<inverse partial perm semigroup of rank 7 with 4 generators>,
<inverse partial perm semigroup of rank 7 with 2 generators>,
<inverse partial perm semigroup of rank 10 with 3 generators>,
<inverse partial perm semigroup of rank 9 with 3 generators>,
<inverse partial perm semigroup of rank 6 with 4 generators>,
<inverse partial perm semigroup of rank 5 with 3 generators>,
<inverse partial perm semigroup of rank 5 with 1 generator> ]
#@if CompareVersionNumbers(ReplacedString(GAPInfo.Version, "dev", ""), "4.15")
gap> CharacterTableOfInverseSemigroup(S[1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, -1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, (1)(3)(4,8) ] ]
gap> CharacterTableOfInverseSemigroup(S[2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, -1, 1, -1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, -1, -1, 6, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, -1, 0, 1, -1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, (1)(2,4,6), (1)(2,6,4),
<identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2,4)(3),
<identity partial perm on [ 2, 5, 7 ]>, (2)(5,7), (2,5,7),
<identity partial perm on [ 2, 5 ]>, (2,5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, (1,6)(3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, (3,7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, -2, 3, -1, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, (1,5)(2,6),
<identity partial perm on [ 1, 3, 6 ]>, (1)(3,6),
<identity partial perm on [ 2, 3, 4 ]>, (2,3,4), (2,4,3),
<identity partial perm on [ 1, 2 ]>, (1,2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, (1,2,6), (1,6,2),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, -1, 0, 1, -1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, (1)(3,4), (1,3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, -E(4), E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, E(4), -E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, -2, 0, 0, 2, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, -2, 0, 0, 10, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, (1)(2,4)(5,7),
(1)(2,5,4,7), (1)(2,7,4,5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, (2,4)(6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, (2,4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, -1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, -1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, -1, 0, 1, -1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, (2)(3,6), (2,3,6),
<identity partial perm on [ 2, 3 ]>, (2,3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, -1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, -1, 1, -1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, -2, 2, 0, 0, 0, 1, -1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, (1,5)(2,3),
<identity partial perm on [ 1, 3, 5 ]>, (1)(3,5),
<identity partial perm on [ 3, 4 ]>, (3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, -1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, (1)(3)(4,8) ] ]
gap> CharacterTableOfInverseSemigroup(S[2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, -1, 1, -1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, -1, -1, 6, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, -1, 0, 1, -1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, (1)(2,4,6), (1)(2,6,4),
<identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2,4)(3),
<identity partial perm on [ 2, 5, 7 ]>, (2)(5,7), (2,5,7),
<identity partial perm on [ 2, 5 ]>, (2,5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, (1,6)(3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, (3,7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, -2, 3, -1, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, (1,5)(2,6),
<identity partial perm on [ 1, 3, 6 ]>, (1)(3,6),
<identity partial perm on [ 2, 3, 4 ]>, (2,3,4), (2,4,3),
<identity partial perm on [ 1, 2 ]>, (1,2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, (1,2,6), (1,6,2),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, -1, 0, 1, -1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, (1)(3,4), (1,3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, -E(4), E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, E(4), -E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, -2, 0, 0, 2, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, -2, 0, 0, 10, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, (1)(2,4)(5,7),
(1)(2,5,4,7), (1)(2,7,4,5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, (2,4)(6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, (2,4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, -1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, -1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, -1, 0, 1, -1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, (2)(3,6), (2,3,6),
<identity partial perm on [ 2, 3 ]>, (2,3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, -1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, -1, 1, -1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, -2, 2, 0, 0, 0, 1, -1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, (1,5)(2,3),
<identity partial perm on [ 1, 3, 5 ]>, (1)(3,5),
<identity partial perm on [ 3, 4 ]>, (3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
#@else
gap> CharacterTableOfInverseSemigroup(S[1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, -1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, (1)(3)(4,8) ] ]
gap> CharacterTableOfInverseSemigroup(S[2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, -1, 1, -1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, -1, -1, 6, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, -1, 0, 1, -1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, (1)(2,4,6), (1)(2,6,4),
<identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2,4)(3),
<identity partial perm on [ 2, 5, 7 ]>, (2)(5,7), (2,5,7),
<identity partial perm on [ 2, 5 ]>, (2,5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, (1,6)(3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, (3,7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, -2, 3, -1, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, (1,5)(2,6),
<identity partial perm on [ 1, 3, 6 ]>, (1)(3,6),
<identity partial perm on [ 2, 3, 4 ]>, (2,3,4), (2,4,3),
<identity partial perm on [ 1, 2 ]>, (1,2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, (1,2,6), (1,6,2),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, -1, 0, 1, -1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, (1)(3,4), (1,3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, -E(4), E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, E(4), -E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, -2, 0, 0, 2, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, -2, 0, 0, 10, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, (1)(2,4)(5,7),
(1)(2,5,4,7), (1)(2,7,4,5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, (2,4)(6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, (2,4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, -1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, -1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, -1, 0, 1, -1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, (2)(3,6), (2,3,6),
<identity partial perm on [ 2, 3 ]>, (2,3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, -1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, -1, 1, -1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, -2, 2, 0, 0, 0, 1, -1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, (1,5)(2,3),
<identity partial perm on [ 1, 3, 5 ]>, (1)(3,5),
<identity partial perm on [ 3, 4 ]>, (3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, -1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, (1)(3)(4,8) ] ]
gap> CharacterTableOfInverseSemigroup(S[2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, -1, 1, -1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, -1, -1, 6, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, -1, 0, 1, -1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, (1)(2,4,6), (1)(2,6,4),
<identity partial perm on [ 1, 2, 3, 4 ]>, (1)(2,4)(3),
<identity partial perm on [ 2, 5, 7 ]>, (2)(5,7), (2,5,7),
<identity partial perm on [ 2, 5 ]>, (2,5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, (1,6)(3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, (3,7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, -2, 3, -1, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, (1,5)(2,6),
<identity partial perm on [ 1, 3, 6 ]>, (1)(3,6),
<identity partial perm on [ 2, 3, 4 ]>, (2,3,4), (2,4,3),
<identity partial perm on [ 1, 2 ]>, (1,2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3), E(3)^2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E(3)^2, E(3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, -1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, (1,2,6), (1,6,2),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, -1, 0, 1, -1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, (1)(3,4), (1,3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, -E(4), E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, -1, E(4), -E(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, -2, 0, 0, 2, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, -2, 0, 0, 10, 6, 6, 3, 3, 3, -1, 3, 1, -1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, (1)(2,4)(5,7),
(1)(2,5,4,7), (1)(2,7,4,5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, (2,4)(6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, (2,4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, -1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, -1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, -1, 0, 1, -1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, (2)(3,6), (2,3,6),
<identity partial perm on [ 2, 3 ]>, (2,3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, -1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, -1, 1, -1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, -2, 2, 0, 0, 0, 1, -1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, (1,5)(2,3),
<identity partial perm on [ 1, 3, 5 ]>, (1)(3,5),
<identity partial perm on [ 3, 4 ]>, (3,4),
<identity partial perm on [ 1, 3 ]>, (1,3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
#@fi
# attrinv: NaturalPartialOrder (for a semigroup), works, 1/1
gap> S := InverseSemigroup([Bipartition([[1, -3], [2, -1], [3, 4, -2, -4]]),
> Bipartition([[1, -1], [2, -3], [3, -2], [4, -4]])]);
<inverse block bijection semigroup of degree 4 with 2 generators>
gap> S := AsSemigroup(IsTransformationSemigroup, S);
<transformation semigroup of size 20, degree 20 with 3 generators>
gap> n := Size(S);;
gap> elts := Elements(S);;
gap> NaturalPartialOrder(S);
[ [ 2, 8, 9, 15, 16, 19 ], [ 9, 16, 19 ], [ 4, 9, 11 ], [ 9 ], [ 9, 16, 18 ],
[ 5, 9, 10, 14, 16, 18 ], [ 9, 13, 20 ], [ 9 ], [ ], [ 9 ], [ 9 ],
[ 9, 11, 13 ], [ 9 ], [ 9, 10, 16 ], [ 8, 9, 16 ], [ 9 ], [ 4, 9, 20 ],
[ 9 ], [ 9 ], [ 9 ] ]
gap> List([1 .. n],
> i -> Filtered([1 .. n],
> j -> i <> j and ForAny(Idempotents(S),
> e -> e * elts[i] = elts[j])));
[ [ 2, 8, 9, 15, 16, 19 ], [ 9, 16, 19 ], [ 4, 9, 11 ], [ 9 ], [ 9, 16, 18 ],
[ 5, 9, 10, 14, 16, 18 ], [ 9, 13, 20 ], [ 9 ], [ ], [ 9 ], [ 9 ],
[ 9, 11, 13 ], [ 9 ], [ 9, 10, 16 ], [ 8, 9, 16 ], [ 9 ], [ 4, 9, 20 ],
[ 9 ], [ 9 ], [ 9 ] ]
gap> last = last2;
true
# attrinv: NaturalPartialOrder (for a semigroup), works, 2
gap> S := Semigroup(SymmetricInverseMonoid(3), rec(acting := true));;
gap> es := IdempotentGeneratedSubsemigroup(S);;
gap> n := Size(es);;
gap> elts := Elements(es);
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>, <identity partial perm on [ 1, 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 2, 3 ]>,
<identity partial perm on [ 1, 3 ]>, <identity partial perm on [ 1, 2, 3 ]>
]
gap> NaturalPartialOrder(es);
[ [ ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1 ], [ 1, 3, 5 ], [ 1, 2, 5 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> List([1 .. n],
> i -> Filtered([1 .. n], j -> elts[j] = elts[j] * elts[i] and i <> j));
[ [ ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1 ], [ 1, 3, 5 ], [ 1, 2, 5 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> last = last2;
true
# attrinv: NaturalPartialOrder (for a semigroup), works, 3
gap> S := Semigroup(SymmetricInverseMonoid(3), rec(acting := true));;
gap> es := IdempotentGeneratedSubsemigroup(S);;
gap> es := AsSemigroup(IsBlockBijectionSemigroup, es);;
gap> n := Size(es);;
gap> elts := Elements(es);;
gap> NaturalPartialOrder(es);
[ [ ], [ 1 ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 3, 4 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> List([1 .. n],
> i -> Filtered([1 .. n], j -> elts[j] = elts[j] * elts[i] and i <> j));
[ [ ], [ 1 ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 3, 4 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> last = last2;
true
# attrinv: NaturalPartialOrder (for a semigroup), error, 1/2
gap> S := Semigroup(
> [Matrix(IsTropicalMinPlusMatrix,
> [[infinity, 0, infinity, 1, 1, infinity, 3, 2, 3],
> [3, 1, 1, infinity, 1, 1, 1, 1, 1], [0, 3, 0, 1, 1, 3, 0, infinity, 1],
> [0, 0, 1, infinity, infinity, 3, 3, 2, 1], [1, 1, 0, 3, 0, 3, 0, 0, 3],
> [0, 2, 3, 1, 0, 0, infinity, 3, infinity],
> [1, 2, 3, 3, 1, 2, infinity, infinity, 3],
> [1, 1, infinity, 3, 3, 1, 1, 1, 1], [1, 2, 0, infinity, 0, 0, 1, 1, 2]],
> 3)]);
<commutative semigroup of 9x9 tropical min-plus matrices with 1 generator>
gap> NaturalPartialOrder(S);
Error, the argument (a semigroup) is not an inverse semigroup
# attrinv: NaturalPartialOrder (for a semigroup), error, 2/2
gap> NaturalPartialOrder(FreeInverseSemigroup(2));
Error, the argument (a semigroup) is not finite
# attrinv: NaturalLeqInverseSemigroup (for a semigroup), error, 1/2
gap> S := Semigroup([
> PBR(
> [[-4, -3, -2, -1, 1, 4, 5, 6], [-6, -5, -4, -3, -2, 2, 6],
> [-6, -4, -3, -1, 1, 2, 4, 5, 6], [-6, 2, 3, 4], [-4, -2, 3, 6],
> [-6, -3, 1, 3, 4, 6]],
> [[-5, -2, -1, 3, 4], [-5, -2, 1, 3, 5],
> [-6, -4, -2, 2, 3, 4, 6], [-5, -3, -1, 2, 4, 6], [-6, -3, 1, 2, 3, 4, 6],
> [-6, -3, 2, 6]]),
> PBR(
> [[-6, -5, -3, -2, -1, 3, 6], [-6, -2, 1, 2, 5], [-6, -5, -4, -1, 1, 6],
> [-6, -5, -4, -2, -1, 2, 5], [-6, -2, -1, 1, 2, 4, 5], [-6, -5, 3, 4, 6]],
> [[-2, 1, 2, 3, 5, 6], [-6, -5, -4, -3, -2, 1, 3, 5],
> [-6, -4, -3, -1, 2, 5, 6], [-5, -2, 3, 4, 5],
> [-6, -5, -4, -3, -2, 1, 2, 3, 5, 6], [-4, 2, 3, 4, 5, 6]])]);
<pbr semigroup of degree 6 with 2 generators>
gap> NaturalLeqInverseSemigroup(S);
Error, the argument (a semigroup) is not an inverse semigroup
# attrinv: NaturalLeqInverseSemigroup (for a semigroup), error, 2/2
gap> NaturalLeqInverseSemigroup(FreeInverseSemigroup(2));
Error, the argument (a semigroup) is not finite
# attrinv: IsGreensDGreaterThanFunc (for an inverse op acting semigroup), 1/1
gap> S := InverseSemigroup(
> [Bipartition([[1, -3], [2, -1], [3, 4, 5, -2, -4, -5]]),
> Bipartition([[1, -1], [2, -3], [3, -4], [4, 5, -2, -5]])]);
<inverse block bijection semigroup of degree 5 with 2 generators>
gap> Size(S);
39
gap> foo := IsGreensDGreaterThanFunc(S);;
gap> foo(S.1, S.2);
false
gap> foo(S.2, S.1);
true
gap> foo(S.1, S.1);
false
# attrinv: PrimitiveIdempotents, inverse, 1/2
gap> S := InverseSemigroup([PartialPerm([1, 2], [3, 1]),
> PartialPerm([1, 2, 3], [1, 3, 4])]);;
gap> Set(PrimitiveIdempotents(S));
[ <identity partial perm on [ 1 ]>, <identity partial perm on [ 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 4 ]> ]
# attrinv: PrimitiveIdempotents, inverse, 2/2
gap> S := InverseSemigroup(
> [PartialPerm([1, 2, 3, 5, 6, 11, 12], [4, 3, 7, 5, 1, 11, 12]),
> PartialPerm([1, 3, 4, 5, 6, 7, 11, 12], [6, 7, 5, 3, 1, 4, 11, 12]),
> PartialPerm([11, 12], [12, 11])]);;
--> --------------------
--> maximum size reached
--> --------------------
