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<h3>References</h3>

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[ABMS15] Araújo, J., Bentz, W., Mitchell, J. D. and Schneider, C.,
The rank of the semigroup of transformations stabilising a partition
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[AMM23] Anagnostopoulou-Merkouri, M., Mesyan, Z. and Mitchell, J. D.,
Properties of congruence lattices of graph inverse semigroups,
International Journal of Algebra and Computation
(2023).


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[Aui12] Auinger, K.,
Krohn–Rhodes complexity of Brauer type
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Portugaliae Mathematica,
69 (4)
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341–360.


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[BDF15] Brouwer, A. E., Draisma, J. and Frenk, B. J.,
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[BFCGOGJ92] Baccelli F. Cohen G. Olsder G. J., Q. J. P.,
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[Bur16] Burrell, S. A.,
The Order Problem for Natural and Tropical Matrix
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MMath project,
University of St Andrews,
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[CP77] Clifford, A. H. and Petrich, M.,
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[DMW18] Donoven, C., Mitchell, J. D. and Wilson, W. A.,
Computing maximal subsemigroups of a finite semigroup,
Journal of Algebra,
505
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559-596.


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[Eas19] East, J.,
<a href="https://www.sciencedirect.com/science/article/pii/S0022404918301403">Presentations for rook partition monoids and algebras and their
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[EEMP19] East, J., Egri-Nagy, A., Mitchell, J. D. and Péresse, Y.,
<a href="https://www.sciencedirect.com/science/article/pii/S0747717118300087">Computing finite semigroups</a>,
J. Symbolic Computation,
92
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110 - 155.


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[Far09] Farlow, K. G.,
Max-Plus Algebra,
Master's thesis,
Virginia Polytechnic Institute and State University,
United States
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[FL98] Fitzgerald, D. G. and Leech, J.,
Dual symmetric inverse monoids and representation theory,
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64
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345-67.


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[FP97] Froidure, V. and Pin, J.-E.,
Algorithms for computing finite semigroups,
 in Foundations of computational mathematics (Rio de
 Janeiro, 1997),
Springer,
Berlin
(1997),
112–126.


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[Gau96] Gaubert, S.,
On the Burnside problem for Semigroups of
 Matrices over the (max, +) Algebra,
Semigroup Forum,
5
(1996),
271-292.


<a id="biBGraham1968aa" name="biBGraham1968aa"></a>

[GGR68] Graham, N., Graham, R. and Rhodes, J.,
Maximal subsemigroups of finite semigroups,
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4
(1968),
203–209.


<a id="biBGraham1968Graph" name="biBGraham1968Graph"></a>

[Gra68] Graham, R.,
On finite 0-simple semigroups and graph theory,
Mathematical systems theory,
2 (4)
(1968),
325–339.


<a id="biBGrood2006aa" name="biBGrood2006aa"></a>

[Gro06] Grood, C.,
<a href="https://dx.doi.org/10.1016/j.jcta.2005.03.006">The rook partition algebra</a>,
J. Combin. Theory Ser. A,
113 (2)
(2006),
325–351.


<a id="biBHowie1995aa" name="biBHowie1995aa"></a>

[How95] Howie, J. M.,
Fundamentals of semigroup theory,
The Clarendon Press Oxford University Press,
London Mathematical Society Monographs. New Series,
12,
New York
(1995),
x+351 pages 
(Oxford Science Publications).


<a id="biBHalverson2005PartitionAlgebras" name="biBHalverson2005PartitionAlgebras"></a>

[HR05] Halverson, T. and Ram, A.,
Partition algebras,
European Journal of Combinatorics,
Elsevier,
26 (6)
(2005),
869–921.


<a id="biBJunttilaKaski" name="biBJunttilaKaski"></a>

[JK07] Junttila, T. and Kaski, P. (Applegate, D., Brodal, G. S., Panario, D. and Sedgewick, R., Eds.),
Engineering an efficient canonical labeling tool for large and sparse
 graphs,
 in Proceedings of the Ninth Workshop on Algorithm Engineering and
 Experiments and the Fourth Workshop on Analytic Algorithms and
 Combinatorics,
SIAM
(2007),
135–149.


<a id="biBKudryavtseva2011aa" name="biBKudryavtseva2011aa"></a>

[KM11] Kudryavtseva, G. and Maltcev, V.,
<a href="https://dx.doi.org/10.5486/PMD.2011.4375">Two generalisations of the symmetric inverse semigroups</a>,
Publ. Math. Debrecen,
78 (2)
(2011),
253–282.


<a id="biBKudryavtseva2015aa" name="biBKudryavtseva2015aa"></a>

[KMU15] Kudryavtseva, G., Maltcev, V. and Umar, A.,
<a href="https://dx.doi.org/10.1080/00927872.2013.876031">Presentation for the partial dual symmetric inverse monoid</a>,
Comm. Algebra,
43 (4)
(2015),
1621–1639.


<a id="biBMartin2011aa" name="biBMartin2011aa"></a>

[MM13] Martin, P. and Mazorchuk, V.,
<a href="https://www.mscand.dk/article/view/15480">Partitioned binary relations</a>,
Mathematica Scandinavica,
113
(2013),
30-52.


<a id="biBMesyan2016" name="biBMesyan2016"></a>

[MM16] Mesyan, Z. and Mitchell, J. D.,
<a href="https://doi.org/10.1007/s00233-016-9793-x">The structure of a graph inverse semigroup</a>,
Semigroup Forum,
Springer Nature,
93 (1)
(2016),
111–130.


<a id="biBPetrich1970aa" name="biBPetrich1970aa"></a>

[Pet70] Petrich, M.,
<a href="https://doi.org/10.1007/BF02573051">The translational hull in semigroups and rings</a>,
Semigroup Forum,
1 (1)
(1970),
283--360.


<a id="biBRadoszewski2010aa" name="biBRadoszewski2010aa"></a>

[RR10] Radoszewski, J. and Rytter, W. (van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J. and Rumpe, B., Eds.),
Efficient Testing of Equivalence of Words in a Free Idempotent Semigroup,
SOFSEM 2010: Theory and Practice of Computer Science,
Springer Berlin Heidelberg,
Berlin, Heidelberg
(2010),
663--671.


<a id="biBSchein1992aa" name="biBSchein1992aa"></a>

[Sch92] Schein, B. M.,
The minimal degree of a finite inverse semigroup,
Trans. Amer. Math. Soc.,
333 (2)
(1992),
877–888.


<a id="biBSimon1978aa" name="biBSimon1978aa"></a>

[Sim78] Simon, I.,
<a href="https://dx.doi.org/10.1109/SFCS.1978.21">Limited Subsets of a Free Monoid</a>,
 in Proceedings of the 19th Annual Symposium on Foundations of
 Computer Science,
IEEE Computer Society,
SFCS '78,
Washington, DC, USA
(1978),
143–150.


<a id="biBWang2019aa" name="biBWang2019aa"></a>

[Wan19] Wang, Z.-P.,
<a href="https://doi.org/10.1016/j.jalgebra.2019.06.020">Congruences on Graph Inverse Semigroups</a>,
Journal of Algebra,
Elsevier {BV},
534
(2019),
51--64.


 

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