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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chap10_mj.html">10</a>  <a href="chap11_mj.html">11</a>  <a href="chap12_mj.html">12</a>  <a href="chap13_mj.html">13</a>  <a href="chap14_mj.html">14</a>  <a href="chapA_mj.html">A</a>  <a href="chapB_mj.html">B</a>  <a href="chapC_mj.html">C</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

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<h3>References</h3>


<p><a id="biBA-A-GS" name="biBA-A-GS"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3942387">AAG19</a></span>]   <b class='BibAuthor'>Abbas, A., Assi, A. and Garc\'{\i}a-S\'{a}nchez, P. A.</b>,
<a href="https://doi.org/10.1007/s13398-018-0538-4"><i class='BibTitle'>Canonical bases of modules over one dimensional
              \(\bold{K}\)-algebras</i></a>,
 <span class='BibJournal'>Rev. R. Acad. Cienc. Exactas F\'{\i}s. Nat. Ser. A Mat.
      RACSAM</span>,
 <em class='BibVolume'>113</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>1121--1139</span>.
</p>


<p><a id="biBnsapp2" name="biBnsapp2"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>ADG20</span>]   <b class='BibAuthor'>Assi, A., D'Anna, M. and Garc\'{\i}a-S\'{a}nchez, P. A.</b>,
<a href="https://doi.org/10.1007/978-3-030-54943-5"><i class='BibTitle'>Numerical semigroups and applications</i></a>,
 <span class='BibPublisher'>Springer, [Cham]</span>,
 <span class='BibSeries'>RSME Springer Series</span>,
 <em class='BibVolume'>3</em>
 (<span class='BibYear'>2020</span>),
 <span class='BibPages'>xiv+138 pages</span>.
</p>


<p><a id="biBAG-GS" name="biBAG-GS"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2729387">AG10</a></span>]   <b class='BibAuthor'>Aguil{\'o}-Gost, F. and Garc{\'{\i}}a-S{\'a}nchez, P. A.</b>,
<a href="https://doi.org/10.37236/410"><i class='BibTitle'>Factoring in embedding dimension three numerical semigroups</i></a>,
 <span class='BibJournal'>Electron. J. Combin.</span>,
 <em class='BibVolume'>17</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2010</span>),
 <span class='BibPages'>Research Paper 13821</span>.
</p>


<p><a id="biBAGS13" name="biBAGS13"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>AG13</span>]   <b class='BibAuthor'>Assi, A. and Garc\'{\i}a-S\'anchez, P. A.</b>,
 <i class='BibTitle'>Constructing the set of complete intersection numerical semigroups
      with a given Frobenius number</i>,
 <span class='BibJournal'>Applicable Algebra in Engineering, Communication and
      Computing</span>
 (<span class='BibYear'>2013</span>).
</p>


<p><a id="biBAGS14" name="biBAGS14"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>AG16a</span>]   <b class='BibAuthor'>Assi, A. and Garc\'{\i}a-S\'anchez, P. A.</b>,
 <i class='BibTitle'>Algorithms for curves with one place at infinity</i>,
 <span class='BibJournal'>Journal of Symbolic Computation</span>,
 <em class='BibVolume'>74</em>
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>475--492</span>.
</p>


<p><a id="biBnsapp" name="biBnsapp"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3558713">AG16b</a></span>]   <b class='BibAuthor'>Assi, A. and Garc\'{\i}a-S\'{a}nchez, P. A.</b>,
<a href="https://doi.org/10.1007/978-3-319-41330-3"><i class='BibTitle'>Numerical semigroups and applications</i></a>,
 <span class='BibPublisher'>Springer, [Cham]</span>,
 <span class='BibSeries'>RSME Springer Series</span>,
 <em class='BibVolume'>1</em>
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>xiv+106 pages</span>.
</p>


<p><a id="biBAGSM14" name="biBAGSM14"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>AGM17</span>]   <b class='BibAuthor'>Assi, A., Garc\'{\i}a-S\'anchez, P. A. and Micale, V.</b>,
 <i class='BibTitle'>Bases of subalgebras of K[[x]] and K[x]</i>,
 <span class='BibJournal'>Journal of Symbolic Computation</span>,
 <em class='BibVolume'>79</em>
 (<span class='BibYear'>2017</span>),
 <span class='BibPages'4--22</span>.
</p>


<p><a id="biBaraujo-neto" name="biBaraujo-neto"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2590388">AN09</a></span>]   <b class='BibAuthor'>Ara\'{u}jo, A. and Neto, O.</b>,
<a href="http://afst.cedram.org/item?id=AFST_2009_6_18_4_797_0"><i class='BibTitle'>Moduli of germs of Legendrian curves</i></a>,
 <span class='BibJournal'>Ann. Fac. Sci. Toulouse Math. (6)</span>,
 <em class='BibVolume'>18</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2009</span>),
 <span class='BibPages'>797--809</span>.
</p>


<p><a id="biBBC77" name="biBBC77"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=0568894">BC77</a></span>]   <b class='BibAuthor'>Bertin, J. and Carbonne, P.</b>,
 <i class='BibTitle'>Semi-groupes d'entiers et application aux branches</i>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>49</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>1977</span>),
 <span class='BibPages'>81--95</span>.
</p>


<p><a id="biBBD-cyclotomic" name="biBBD-cyclotomic"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1034734">BD89</a></span>]   <b class='BibAuthor'>Bradford, R. J. and Davenport, J. H.</b>,
<a href="https://doi.org/10.1007/3-540-51084-2_22"><i class='BibTitle'>Effective tests for cyclotomic polynomials</i></a>,
  in  <i class='BibBooktitle'>Symbolic and algebraic computation (Rome,
      1988)</i>,
 <span class='BibPublisher'>Springer, Berlin</span>,
 <span class='BibSeries'>Lecture Notes in Comput. Sci.</span>,
 <em class='BibVolume'>358</em>
 (<span class='BibYear'>1989</span>),
 <span class='BibPages'>244--251</span>.
</p>


<p><a id="biBBDF97" name="biBBDF97"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BDF97</span>]   <b class='BibAuthor'>Barucci, V., Dobbs, D. D. and Fontana, M.</b>,
 <i class='BibTitle'>Maximality properties in numerical semigroups and applications to
 one-dimensional analytically irreducible local domains</i>,
 <span class='BibPublisher'>American Mathematical Society</span>,
 <span class='BibSeries'>Memoirs of the American Mathematical Society</span> (<span class='BibNumber'>598</span>)
 (<span class='BibYear'>1997</span>).
</p>


<p><a id="biBB-DA-F-2" name="biBB-DA-F-2"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1747441">BDF00a</a></span>]   <b class='BibAuthor'>Barucci, V., D'Anna, M. and Fr\"{o}berg, R.</b>,
<a href="https://doi.org/10.1016/S0022-4049(98)00160-1"><i class='BibTitle'>Analytically unramified one-dimensional semilocal rings and
              their value semigroups</i></a>,
 <span class='BibJournal'>J. Pure Appl. Algebra</span>,
 <em class='BibVolume'>147</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2000</span>),
 <span class='BibPages'>215--254</span>.
</p>


<p><a id="biBB-DA-F-1" name="biBB-DA-F-1"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1767576">BDF00b</a></span>]   <b class='BibAuthor'>Barucci, V., D'Anna, M. and Fr\"{o}berg, R.</b>,
<a href="https://doi.org/10.1080/00927870008827044"><i class='BibTitle'>The semigroup of values of a one-dimensional local ring with
              two minimal primes</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>28</em> (<span class='BibNumber'>8</span>)
 (<span class='BibYear'>2000</span>),
 <span class='BibPages'>3607--3633</span>.
</p>


<p><a id="biBBF97" name="biBBF97"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BF97</span>]   <b class='BibAuthor'>Barucci, V. and Fr\"oberg, R.</b>,
 <i class='BibTitle'>One-dimensional almost Gorenstein Rings</i>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>188</em>
 (<span class='BibYear'>1997</span>),
 <span class='BibPages'>418--442</span>.
</p>


<p><a id="biBBF06" name="biBBF06"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BF06</span>]   <b class='BibAuthor'>Barucci, V. and Fr\"oberg, R.</b>,
 <i class='BibTitle'>Associated graded rings of one-dimensional analytically
irreducible rings</i>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>304</em>
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>349--358</span>.
</p>


<p><a id="biBBA-GS" name="biBBA-GS"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2214415">BG06</a></span>]   <b class='BibAuthor'>Bras-Amor{\'o}s, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.</b>,
<a href="https://doi.org/10.1016/j.laa.2005.11.007"><i class='BibTitle'>Patterns on numerical semigroups</i></a>,
 <span class='BibJournal'>Linear Algebra Appl.</span>,
 <em class='BibVolume'>414</em> (<span class='BibNumber'>2-3</span>)
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>652--669</span>.
</p>


<p><a id="biBB-GS-G" name="biBB-GS-G"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BGG11</span>]   <b class='BibAuthor'>Blanco, V., Garc\'{\i}a-S\'anchez, P. A. and Geroldinger, A.</b>,
 <i class='BibTitle'>Semigroup-theoretical characterizations of arithmetical invariants
      with applications to numerical monoids and Krull monoids</i>,
 <span class='BibJournal'>Illinois J. Math.</span>,
 <em class='BibVolume'>55</em>
 (<span class='BibYear'>2011</span>),
 <span class='BibPages'>1385--1414</span>.
</p>


<p><a id="biBBH" name="biBBH"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3053780">BH13</a></span>]   <b class='BibAuthor'>Bryant, L. and Hamblin, J.</b>,
<a href="https://doi.org/10.1007/s00233-012-9448-5"><i class='BibTitle'>The maximal denumerant of a numerical semigroup</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>86</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>571--582</span>.
</p>


<p><a id="biBNormaliz" name="biBNormaliz"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BIRC14</span>]   <b class='BibAuthor'>Bruns, W., Ichim, B., R\"omer, T. and C., S.</b>,
 <i class='BibTitle'>Normaliz. Algorithms for rational cones and affine monoids</i>
 (<span class='BibYear'>2014</span>),
<span class='BibHowpublished'>\url{https://www.normaliz.uni-osnabrueck.de}</span>.
</p>


<p><a id="biBB-P-ON" name="biBB-P-ON"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3647965">BOP17</a></span>]   <b class='BibAuthor'>Barron, T., O'Neill, C. and Pelayo, R.</b>,
<a href="https://doi.org/10.1090/mcom/3160"><i class='BibTitle'>On dynamic algorithms for factorization invariants in
              numerical monoids</i></a>,
 <span class='BibJournal'>Math. Comp.</span>,
 <em class='BibVolume'>86</em> (<span class='BibNumber'>307</span>)
 (<span class='BibYear'>2017</span>),
 <span class='BibPages'>2429--2447</span>.
</p>


<p><a id="biBBOR18" name="biBBOR18"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BOR18</span>]   <b class='BibAuthor'>Branco, M., Ojeda, I. and Rosales, J. C.</b>,
 <i class='BibTitle'>Almost symmetric numerical semigroups with a given Frobenus number
      and type</i>,
 <span class='BibJournal'>preprint</span>
 (<span class='BibYear'>2018</span>).
</p>


<p><a id="biBBOR19" name="biBBOR19"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=4301804">BOR21</a></span>]   <b class='BibAuthor'>Branco, M. B., Ojeda, I. and Rosales, J. C.</b>,
<a href="https://doi.org/10.4171/pm/2064"><i class='BibTitle'>The set of numerical semigroups of a given multiplicity and
              Frobenius number</i></a>,
 <span class='BibJournal'>Port. Math.</span>,
 <em class='BibVolume'>78</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2021</span>),
 <span class='BibPages'>147--167</span>.
</p>


<p><a id="biBRos05" name="biBRos05"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2476582">BR09</a></span>]   <b class='BibAuthor'>Bullejos, M. and Rosales, J. C.</b>,
<a href="https://doi.org/10.1090/S0025-5718-08-02173-X"><i class='BibTitle'>Proportionally modular Diophantine inequalities and the
              Stern-Brocot tree</i></a>,
 <span class='BibJournal'>Math. Comp.</span>,
 <em class='BibVolume'>78</em> (<span class='BibNumber'>266</span>)
 (<span class='BibYear'>2009</span>),
 <span class='BibPages'>1211--1226</span>.
</p>


<p><a id="biBBR13" name="biBBR13"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3199729">BR13</a></span>]   <b class='BibAuthor'>Blanco, V. and Rosales, J. C.</b>,
<a href="https://doi.org/10.1515/form.2011.151"><i class='BibTitle'>The tree of irreducible numerical semigroups with fixed
              Frobenius number</i></a>,
 <span class='BibJournal'>Forum Math.</span>,
 <em class='BibVolume'>25</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>1249--1261</span>.
</p>


<p><a id="biBBr-acute" name="biBBr-acute"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2094884">Bra04</a></span>]   <b class='BibAuthor'>Bras-Amor\'os, M.</b>,
<a href="https://doi.org/10.1109/TIT.2004.828104"><i class='BibTitle'>Acute semigroups, the order bound on the minimum distance, and
              the Feng-Rao improvements</i></a>,
 <span class='BibJournal'>IEEE Trans. Inform. Theory</span>,
 <em class='BibVolume'>50</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2004</span>),
 <span class='BibPages'>1282--1289</span>.
</p>


<p><a id="biBB-A08" name="biBB-A08"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bra08</span>]   <b class='BibAuthor'>Bras-Amor\'os, M.</b>,
 <i class='BibTitle'>Fibonacci-like behavior of the number of numerical semigroups of
 a given genus</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>76</em>
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>379--384</span>.
</p>


<p><a id="biBbras-ns-codes" name="biBbras-ns-codes"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3288285">Bra13</a></span>]   <b class='BibAuthor'>Bras-Amor\'{o}s, M.</b>,
<a href="https://doi.org/10.1142/9789814335768_0005"><i class='BibTitle'>Numerical semigroups and codes</i></a>,
  in  <i class='BibBooktitle'>Algebraic geometry modeling in information theory</i>,
 <span class='BibPublisher'>World Sci. Publ., Hackensack, NJ</span>,
 <span class='BibSeries'>Ser. Coding Theory Cryptol.</span>,
 <em class='BibVolume'>8</em>
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>167--218</span>.
</p>


<p><a id="biBBr" name="biBBr"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2675524">Bry10</a></span>]   <b class='BibAuthor'>Bryant, L.</b>,
<a href="https://doi.org/10.1080/00927870903025993"><i class='BibTitle'>Goto numbers of a numerical semigroup ring and the
              Gorensteiness of associated graded rings</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>38</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2010</span>),
 <span class='BibPages'>2092--2128</span>.
</p>


<p><a id="biBdilatation" name="biBdilatation"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3917961">BS19</a></span>]   <b class='BibAuthor'>Barucci, V. and Strazzanti, F.</b>,
<a href="https://doi.org/10.1007/s00233-018-9922-9"><i class='BibTitle'>Dilatations of numerical semigroups</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>98</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>251--260</span>.
</p>


<p><a id="biBR-GS-GG-B" name="biBR-GS-GG-B"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CAGB02</span>]   <b class='BibAuthor'>C., R., Garc\'{\i}a-S\'anchezP. A., Garc\'{\i}a-Garc\'{\i}a, J. I., and Branco, M. B.</b>,
<a href="http://journals.cambridge.org/article_S0024610701003052"><i class='BibTitle'>SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS</i></a>,
 <span class='BibJournal'>Journal of the London Mathematical Society</span>,
 <em class='BibVolume'>65</em>
 (<span class='BibYear'>2002</span>),
 <span class='BibPages'>611--623</span>.
</p>


<p><a id="biBCJZ" name="biBCJZ"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CBJZA13</span>]   <b class='BibAuthor'>Cortadellas Ben\'{\i}tez, T., Jafari, R. and Zarzuela Armengou, S.</b>,
 <i class='BibTitle'>On teh Ap\'ery sets of monomial curves</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>86</em>
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>289--320</span>.
</p>


<p><a id="biBMR1283022" name="biBMR1283022"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=MR1283022">CD94</a></span>]   <b class='BibAuthor'>Contejean, E. and Devie, H.</b>,
 <i class='BibTitle'>An efficient incremental algorithm for solving systems of
               linear Diophantine equations</i>,
 <span class='BibJournal'>Inform. and Comput.</span>,
 <em class='BibVolume'>113</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>1994</span>),
 <span class='BibPages'>143--172</span>.
</p>


<p><a id="biBSingularpackage" name="biBSingularpackage"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CdG12</span>]   <b class='BibAuthor'>Costantini, M. and de Graaf, W.</b>,
 <i class='BibTitle'>GAP package singular; the GAP interface to Singular</i>
 (<span class='BibYear'>2012</span>),
<span class='BibHowpublished'>\url{https://gap-system.org/Packages/singular.html}</span>.
</p>


<p><a id="biBC-F-U" name="biBC-F-U"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CFR18</span>]   <b class='BibAuthor'>Cisto, C., Failla, G. and R., U.</b>,
 <i class='BibTitle'>On the generators of a generalized numerical semigroup</i>,
 <span class='BibJournal'>Analele Stiintifice ale Universitatii Ovidius Constanta</span>
 (<span class='BibYear'>2018</span>).
</p>


<p><a id="biBCGL" name="biBCGL"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CGD07</span>]   <b class='BibAuthor'>Chapman, S. T., Garc\'{\i}a-S\'anchez, P. A. and D., L.</b>,
 <i class='BibTitle'>The catenary and tame degree of numerical semigroups</i>,
 <span class='BibJournal'>Forum Math.</span>
 (<span class='BibYear'>2007</span>),
 <span class='BibPages'>1--13</span>.
</p>


<p><a id="biBC-GS-HP-M" name="biBC-GS-HP-M"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CGHM19</span>]   <b class='BibAuthor'>Ciolan, E.-A., Garc\'{i}a-S\'{a}nchez, P. A., Herrera-Poyatos, A. and Moree, P.</b>,
 <i class='BibTitle'>Cyclotomic exponent sequences of numerical semigroups</i>,
 <span class='BibJournal'>preprint</span>
 (<span class='BibYear'>2019</span>).
</p>


<p><a id="biBCGLPR" name="biBCGLPR"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CGL+06</span>]   <b class='BibAuthor'>Chapman, S. T., Garc\'{\i}a-S\'anchez, P. A., Llena, D., Ponomarenko, V. and Rosales, J. C.</b>,
 <i class='BibTitle'>The catenary and tame degree in finitely generated commutative
      cancellative
 monoids</i>,
 <span class='BibJournal'>Manuscripta Math.</span>,
 <em class='BibVolume'>120</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>253--264</span>.
</p>


<p><a id="biBC-GS-M" name="biBC-GS-M"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3483156">CGM16</a></span>]   <b class='BibAuthor'>Ciolan, E.-A., Garc\'{i}a-S\'{a}nchez, P. A. and Moree, P.</b>,
<a href="https://doi.org/10.1137/140989479"><i class='BibTitle'>Cyclotomic numerical semigroups</i></a>,
 <span class='BibJournal'>SIAM J. Discrete Math.</span>,
 <em class='BibVolume'>30</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>650--668</span>.
</p>


<p><a id="biBCHM06" name="biBCHM06"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CHM06</span>]   <b class='BibAuthor'>Chapman, S. T., Holden, M. T. and Moore, T. A.</b>,
 <i class='BibTitle'>Full elasticity in atomic monoids and integral domains</i>,
 <span class='BibJournal'>Rocky Mountain J. Math.</span>,
 <em class='BibVolume'>36</em> (<span class='BibNumber'>5</span>)
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>1437--1455</span>.
</p>


<p><a id="biBCHRA" name="biBCHRA"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3110597">CRA13</a></span>]   <b class='BibAuthor'>Chappelon, J. and Ram{\'{\i}}rez Alfons{\'{\i}}n, J. L.</b>,
<a href="https://doi.org/10.1007/s00233-012-9458-3"><i class='BibTitle'>On the M\"obius function of the locally finite poset
              associated with a numerical semigroup</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>87</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>313--330</span>.
</p>


<p><a id="biBDM" name="biBDM"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=949819">DdlM88</a></span>]   <b class='BibAuthor'>Delgado de la Mata, F.</b>,
<a href="https://doi.org/10.1007/BF01258440"><i class='BibTitle'>Gorenstein curves and symmetry of the semigroup of values</i></a>,
 <span class='BibJournal'>Manuscripta Math.</span>,
 <em class='BibVolume'>61</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>1988</span>),
 <span class='BibPages'>285--296</span>.
</p>


<p><a id="biBMR3493240" name="biBMR3493240"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3493240">DG16</a></span>]   <b class='BibAuthor'>Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.</b>,
 <i class='BibTitle'>numericalsgps, a GAP package for numerical
              semigroups</i>,
 <span class='BibJournal'>ACM Commun. Comput. Algebra</span>,
 <em class='BibVolume'>50</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>12--24</span>.
</p>


<p><a id="biBDA-G-H" name="biBDA-G-H"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1842007">DGH01</a></span>]   <b class='BibAuthor'>D'Anna, M., Guerrieri, A. and Heinzer, W.</b>,
<a href="https://doi.org/10.1081/AGB-100001550"><i class='BibTitle'>Invariants of ideals having principal reductions</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>29</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2001</span>),
 <span class='BibPages'>889--906</span>.
</p>


<p><a id="biBJMDA" name="biBJMDA"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2325970">DGM06</a></span>]   <b class='BibAuthor'>Delgado, M., Garc\'{\i}a-S\'anchez, P. A. and Morais, J.</b>,
 <i class='BibTitle'>On the GAP package numericalsgps</i>,
  in  <i class='BibBooktitle'>Fifth Conference on Discrete Mathematics and
      Computer
              Science (Spanish)</i>,
 <span class='BibPublisher'>Univ. Valladolid</span>,
 <span class='BibSeries'>Ciencias (Valladolid)</span>,
 <em class='BibVolume'>23</em>,
 <span class='BibAddress'>Secr. Publ. Intercamb. Ed., Valladolid</span>
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>271--278</span>.
</p>


<p><a id="biBDGSM" name="biBDGSM"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3786416">DGMT18</a></span>]   <b class='BibAuthor'>D'Anna, M., Garc\'{\i}a-S\'{a}nchez, P. A., Micale, V. and Tozzo, L.</b>,
<a href="https://doi.org/10.1142/S0218196718500091"><i class='BibTitle'>Good subsemigroups of \(\Bbb N^n\)</i></a>,
 <span class='BibJournal'>Internat. J. Algebra Comput.</span>,
 <em class='BibVolume'>28</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>179--206</span>.
</p>


<p><a id="biBSingular" name="biBSingular"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DGPS12</span>]   <b class='BibAuthor'>Decker, W., Greuel, G.-M., Pfister, G. and Sch\"onemann, H.</b>,
 <i class='BibTitle'>\sc Singular 3-1-6 --- A computer algebra system
      for polynomial computations</i>
 (<span class='BibYear'>2012</span>),
<span class='BibHowpublished'>\url{https://www.singular.uni-kl.de}</span>.
</p>


<p><a id="biBDGSRP15" name="biBDGSRP15"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DGR16</span>]   <b class='BibAuthor'>Delgado, M., Garc{\'{\i}}a-S{\'a}nchez, P. A. and Robles-P{\'e}rez, A. M.</b>,
 <i class='BibTitle'>Numerical semigroups with a given set of pseudo-Frobenius
      numbers</i>,
 <span class='BibJournal'>LMS J. Comput. Math.</span>,
 <em class='BibVolume'>19</em>
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>186--205</span>.
</p>


<p><a id="biBDA-M-S" name="biBDA-M-S"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2813470">DMS11</a></span>]   <b class='BibAuthor'>D'Anna, M., Micale, V. and Sammartano, A.</b>,
 <i class='BibTitle'>On the associated graded ring of a semigroup ring</i>,
 <span class='BibJournal'>J. Commut. Algebra</span>,
 <em class='BibVolume'>3</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2011</span>),
 <span class='BibPages'>147--168</span>.
</p>


<p><a id="biBDAMSwhen" name="biBDAMSwhen"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3010100">DMS13</a></span>]   <b class='BibAuthor'>D'Anna, M., Micale, V. and Sammartano, A.</b>,
<a href="https://doi.org/10.1016/j.jpaa.2012.09.024"><i class='BibTitle'>When the associated graded ring of a semigroup ring is
              complete intersection</i></a>,
 <span class='BibJournal'>J. Pure Appl. Algebra</span>,
 <em class='BibVolume'>217</em> (<span class='BibNumber'>6</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>1007--1017</span>.
</p>


<p><a id="biBDAMSClasses" name="biBDAMSClasses"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3189106">DMS14</a></span>]   <b class='BibAuthor'>D'Anna, M., Micale, V. and Sammartano, A.</b>,
<a href="https://doi.org/10.1007/s00233-013-9547-y"><i class='BibTitle'>Classes of complete intersection numerical semigroups</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>88</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2014</span>),
 <span class='BibPages'>453--467</span>.
</p>


<p><a id="biBDA-M-M" name="biBDA-M-M"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DMV09</span>]   <b class='BibAuthor'>D'Anna, M., Mezzasalma, M. and V., M.</b>,
 <i class='BibTitle'>On the Buchsbaumness of the associated graded ring of a
      one-dimensional local ring</i>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>37</em>
 (<span class='BibYear'>2009</span>),
 <span class='BibPages'>1594--1603</span>.
</p>


<p><a id="biBduplication" name="biBduplication"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3079777">DS13</a></span>]   <b class='BibAuthor'>D'Anna, M. and Strazzanti, F.</b>,
<a href="https://doi.org/10.1007/s00233-012-9451-x"><i class='BibTitle'>The numerical duplication of a numerical semigroup</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>87</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>149--160</span>.
</p>


<p><a id="biBgas-semigroups" name="biBgas-semigroups"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=4283166">DS21</a></span>]   <b class='BibAuthor'>D'Anna, M. and Strazzanti, F.</b>,
<a href="https://doi.org/10.1080/00927872.2021.1900213"><i class='BibTitle'>Almost canonical ideals and GAS numerical semigroups</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>49</em> (<span class='BibNumber'>8</span>)
 (<span class='BibYear'>2021</span>),
 <span class='BibPages'>3534--3551</span>.
</p>


<p><a id="biBE01" name="biBE01"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Eli01</span>]   <b class='BibAuthor'>Elias, J.</b>,
 <i class='BibTitle'>On the deep structure of the blowing-up of curve
      singularities</i>,
 <span class='BibJournal'>Math. Proc.  Camb. Phil. Soc.</span>,
 <em class='BibVolume'>131</em>
 (<span class='BibYear'>2001</span>),
 <span class='BibPages'>227--240</span>.
</p>


<p><a id="biBE" name="biBE"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3836842">Eli18</a></span>]   <b class='BibAuthor'>Eliahou, S.</b>,
<a href="https://doi.org/10.4171/JEMS/807"><i class='BibTitle'>Wilf's conjecture and Macaulay's theorem</i></a>,
 <span class='BibJournal'>J. Eur. Math. Soc. (JEMS)</span>,
 <em class='BibVolume'>20</em> (<span class='BibNumber'>9</span>)
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>2105--2129</span>.
</p>


<p><a id="biBMR1394747" name="biBMR1394747"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1394747">ES96</a></span>]   <b class='BibAuthor'>Eisenbud, D. and Sturmfels, B.</b>,
<a href="https://doi.org/10.1215/S0012-7094-96-08401-X"><i class='BibTitle'>Binomial ideals</i></a>,
 <span class='BibJournal'>Duke Math. J.</span>,
 <em class='BibVolume'>84</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>1996</span>),
 <span class='BibPages'>1--45</span>.
</p>


<p><a id="biBFGH87" name="biBFGH87"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>FGR87</span>]   <b class='BibAuthor'>Fr\"oberg, R., Gottlieb, C. and R., H.</b>,
 <i class='BibTitle'>On numerical semigroups</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>35</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>1987</span>),
 <span class='BibPages'>63--83</span>.
</p>


<p><a id="biBGHKb" name="biBGHKb"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GH06</span>]   <b class='BibAuthor'>Geroldinger, A. and Halter-Koch, F.</b>,
 <i class='BibTitle'>Non-unique Factorizations: Algebraic, Combinatorial and
Analytic Theory</i>,
 <span class='BibPublisher'>Chapman \& Hall/CRC</span>
 (<span class='BibYear'>2006</span>).
</p>


<p><a id="biBarf-frob-gen" name="biBarf-frob-gen"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GHKR17</span>]   <b class='BibAuthor'>Garc{\'{\i}}a-S{\'a}nchez, P. A., Heredia, B. A., Karakas, H. I. and Rosales, J. C.</b>,
 <i class='BibTitle'>Parametrizing Arf numerical semigroups</i>,
 <span class='BibJournal'>J. Algebra Appl.</span>,
 <em class='BibVolume'>16</em>
 (<span class='BibYear'>2017</span>),
 <span class='BibPages'>1750209 (31 pages)</span>.
</p>


<p><a id="biBNmzInterface" name="biBNmzInterface"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GHS14</span>]   <b class='BibAuthor'>Gutsche, S., Horn, M. and S\"oger, C.</b>,
 <i class='BibTitle'>NormalizInterface for GAP</i>
 (<span class='BibYear'>2014</span>),
<span class='BibHowpublished'>\url{https://github.com/gap-packages/NormalizInterface}</span>.
</p>


<p><a id="biBGG-MF-VT" name="biBGG-MF-VT"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GMV15</span>]   <b class='BibAuthor'>Garc\'{\i}a-Garc\'{\i}a, J. I., Moreno-Fr\'{\i}as, M. A. and Vigneron-Tenorio, A.</b>,
 <i class='BibTitle'>Computation of Delta sets of numerical monoids</i>,
 <span class='BibJournal'>Monatsh. Math. </span>,
 <em class='BibVolume'>178</em>
 (<span class='BibYear'>2015</span>),
 <span class='BibPages'>457--472</span>.
</p>


<p><a id="biBGS-O" name="biBGS-O"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GO10</span>]   <b class='BibAuthor'>Garc\'{\i}a-S\'anchez, P. A. and Ojeda, I.</b>,
 <i class='BibTitle'>Uniquely presented finitely generated commutative monoids</i>,
 <span class='BibJournal'>Pacific J. Math.</span>,
 <em class='BibVolume'>249</em>
 (<span class='BibYear'>2010</span>),
 <span class='BibPages'>91--105</span>.
</p>


<p><a id="biBGSONW" name="biBGSONW"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3910672">GOW19</a></span>]   <b class='BibAuthor'>Garc\'{\i}a-S\'{a}nchez, P. A., O'Neill, C. and Webb, G.</b>,
<a href="https://doi.org/10.1142/S0219498819500191"><i class='BibTitle'>The computation of factorization invariants for affine
              semigroups</i></a>,
 <span class='BibJournal'>J. Algebra Appl.</span>,
 <em class='BibVolume'>18</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>195001921</span>.
</p>


<p><a id="biBGSOSN" name="biBGSOSN"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3040805">GSOSt13</a></span>]   <b class='BibAuthor'>Garc{\'{\i}}a S{\'a}nchez, P. A., Ojeda, I. and S{\'a}nchez-R. -Navarro, A.</b>,
<a href="https://doi.org/10.1142/S0218196713500033"><i class='BibTitle'>Factorization invariants in half-factorial affine semigroups</i></a>,
 <span class='BibJournal'>Internat. J. Algebra Comput.</span>,
 <em class='BibVolume'>23</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2013</span>),
 <span class='BibPages'>111--122</span>.
</p>


<p><a id="biB4ti2Interface" name="biB4ti2Interface"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Gut</span>]   <b class='BibAuthor'>Gutsche, S.</b>,
 <i class='BibTitle'>4ti2Interface, A link to 4ti2</i>,
<span class='BibHowpublished'>\url{https://www.gap-system.org/Packages/4ti2interface.html}</span>.
</p>


<p><a id="biBMR0269762" name="biBMR0269762"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=0269762">Her70</a></span>]   <b class='BibAuthor'>Herzog, J.</b>,
 <i class='BibTitle'>Generators and relations of abelian semigroups and semigroup
              rings. </i>,
 <span class='BibJournal'>Manuscripta Math.</span>,
 <em class='BibVolume'>3</em>
 (<span class='BibYear'>1970</span>),
 <span class='BibPages'>175--193</span>.
</p>


<p><a id="biBtrace-canonical" name="biBtrace-canonical"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=4013970">HHS19</a></span>]   <b class='BibAuthor'>Herzog, J., Hibi, T. and Stamate, D. I.</b>,
<a href="https://doi.org/10.1007/s11856-019-1898-y"><i class='BibTitle'>The trace of the canonical module</i></a>,
 <span class='BibJournal'>Israel J. Math.</span>,
 <em class='BibVolume'>233</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2019</span>),
 <span class='BibPages'>133--165</span>.
</p>


<p><a id="biBtrace-ideal" name="biBtrace-ideal"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=4305507">HHS21</a></span>]   <b class='BibAuthor'>Herzog, J., Hibi, T. and Stamate, D. I.</b>,
<a href="https://doi.org/10.1007/s00233-021-10205-x"><i class='BibTitle'>Canonical trace ideal and residue for numerical semigroup
              rings</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>103</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2021</span>),
 <span class='BibPages'>550--566</span>.
</p>


<p><a id="biBHS04" name="biBHS04"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>HS04</span>]   <b class='BibAuthor'>Herzinger, K. and Sanford, R.</b>,
 <i class='BibTitle'>Minimal Generating Sets for Relative Ideals in Numerical Semigroups
      of Multiplicity Eight</i>,
 <span class='BibJournal'>Communications in Algebra</span>,
 <em class='BibVolume'>32</em> (<span class='BibNumber'>12</span>)
 (<span class='BibYear'>2004</span>),
 <span class='BibPages'>4713-4731</span>.
</p>


<p><a id="biBhomogeneous-ns" name="biBhomogeneous-ns"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3852775">JZA18</a></span>]   <b class='BibAuthor'>Jafari, R. and Zarzuela Armengou, S.</b>,
<a href="https://doi.org/10.1007/s00233-018-9941-6"><i class='BibTitle'>Homogeneous numerical semigroups</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>97</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2018</span>),
 <span class='BibPages'>278--306</span>.
</p>


<p><a id="biBkomatsu" name="biBkomatsu"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Kom24</span>]   <b class='BibAuthor'>Komatsu, T.</b>,
<a href="https://doi.org/10.1007/s13398-024-01556-5"><i class='BibTitle'>On the determination of p-Frobenius and related numbers using the
      p-Ap\'ery set</i></a>,
 <span class='BibJournal'>Revista de la Real Academia de Ciencias Exactas, F{\'\i}sicas y
      Naturales. Serie A. Matem{\'a}ticas</span>,
 <em class='BibVolume'>118</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2024</span>),
 <span class='BibPages'>58</span>.
</p>


<p><a id="biBKP95" name="biBKP95"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1391031">KP95</a></span>]   <b class='BibAuthor'>Kirfel, C. and Pellikaan, R.</b>,
<a href="https://doi.org/10.1109/18.476245"><i class='BibTitle'>The minimum distance of codes in an array coming from
              telescopic semigroups</i></a>,
 <span class='BibJournal'>IEEE Trans. Inform. Theory</span>,
 <em class='BibVolume'>41</em> (<span class='BibNumber'>6, part 1</span>)
 (<span class='BibYear'>1995</span>),
 <span class='BibPages'>1720--1732</span><br />
(<span class='BibNote'>Special issue on algebraic geometry codes</span>).
</p>


<p><a id="biBK-W" name="biBK-W"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3274840">KW14</a></span>]   <b class='BibAuthor'>Kunz, E. and Waldi, R.</b>,
<a href="https://doi.org/10.1007/s00233-014-9599-7"><i class='BibTitle'>Geometrical illustration of numerical semigroups and of some
              of their invariants</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>89</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2014</span>),
 <span class='BibPages'>664--691</span>.
</p>


<p><a id="biBVMic02" name="biBVMic02"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Mic02</span>]   <b class='BibAuthor'>Micale, V.</b>,
 <i class='BibTitle'>On monomial semigroups</i>,
 <span class='BibJournal'>Communications in Algebra</span>,
 <em class='BibVolume'>30</em>
 (<span class='BibYear'>2002</span>),
 <span class='BibPages'>4687 - 4698</span>.
</p>


<p><a id="biBG-K" name="biBG-K"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>MK17</span>]   <b class='BibAuthor'>Matsuoka, N. and Kumashiro, S.</b>,
<a href="https://www.ugr.es/~imns2010/2018/Talks/NMatsuoka.pdf"><i class='BibTitle'>The generalized Gorenstein property and numerical semigroup rings
      obtained by gluing</i></a>,
 <span class='BibJournal'>IMNS2010 - abstracts</span>
 (<span class='BibYear'>2017</span>).
</p>


<p><a id="biBM" name="biBM"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3295662">Mor14</a></span>]   <b class='BibAuthor'>Moree, P.</b>,
<a href="https://doi.org/10.4169/amer.math.monthly.121.10.890"><i class='BibTitle'>Numerical semigroups, cyclotomic polynomials, and Bernoulli
              numbers</i></a>,
 <span class='BibJournal'>Amer. Math. Monthly</span>,
 <em class='BibVolume'>121</em> (<span class='BibNumber'>10</span>)
 (<span class='BibYear'>2014</span>),
 <span class='BibPages'>890--902</span>.
</p>


<p><a id="biBRFMatrix" name="biBRFMatrix"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3484144">Mos16</a></span>]   <b class='BibAuthor'>Moscariello, A.</b>,
<a href="https://doi.org/10.1016/j.jalgebra.2016.02.019"><i class='BibTitle'>On the type of an almost Gorenstein monomial curve</i></a>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>456</em>
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>266--277</span>.
</p>


<p><a id="biBMC-O-T" name="biBMC-O-T"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3369384">MOT15</a></span>]   <b class='BibAuthor'>M{\'a}rquez-Campos, G., Ojeda, I. and Tornero, J. M.</b>,
<a href="https://doi.org/10.1007/s00233-014-9631-y"><i class='BibTitle'>On the computation of the Ap\'ery set of numerical monoids
              and affine semigroups</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>91</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2015</span>),
 <span class='BibPages'>139--158</span>.
</p>


<p><a id="biBnearly-almost" name="biBnearly-almost"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>MS21</span>]   <b class='BibAuthor'>Moscariello, A. and Strazzanti, F.</b>,
 <i class='BibTitle'>Nearly Gorenstein vs almost Gorenstein affine monomial curves</i>,
 <span class='BibJournal'>Mediterranean Journal of Mathematics</span>,
 <span class='BibPublisher'>Springer</span>,
 <em class='BibVolume'>18</em> (<span class='BibNumber'>4</span>)
 (<span class='BibYear'>2021</span>),
 <span class='BibPages'>1--14</span>.
</p>


<p><a id="biBM-Z" name="biBM-Z"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=4178261">MZ20</a></span>]   <b class='BibAuthor'>Maugeri, N. and Zito, G.</b>,
 <i class='BibTitle'>Embedding dimension of a good semigroup</i>,
  in  <i class='BibBooktitle'>Numerical semigroups</i>,
 <span class='BibPublisher'>Springer, Cham</span>,
 <span class='BibSeries'>Springer INdAM Ser.</span>,
 <em class='BibVolume'>40</em>
 (<span class='BibYear'>[2020] \copyright 2020</span>),
 <span class='BibPages'>197--230</span>.
</p>


<p><a id="biBPH" name="biBPH"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Phi10</span>]   <b class='BibAuthor'>Philipp, A.</b>,
 <i class='BibTitle'>A characterization of arithmetical invariants by the monoid of
      relations</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>81</em>
 (<span class='BibYear'>2010</span>),
 <span class='BibPages'>424--434</span>.
</p>


<p><a id="biBRGGU03" name="biBRGGU03"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RAGU03</span>]   <b class='BibAuthor'>Rosales, J. C., A., G.-S. P., Garc\'{\i}a-Garc\'{\i}a, J. I. and Urbano-Blanco, J. M.</b>,
 <i class='BibTitle'>Proportionally modular Diophantine inequalities</i>,
 <span class='BibJournal'>J. Number Theory</span>,
 <em class='BibVolume'>103</em>
 (<span class='BibYear'>2003</span>),
 <span class='BibPages'>281-294</span>.
</p>


<p><a id="biBRB03" name="biBRB03"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RB03</span>]   <b class='BibAuthor'>Rosales, J. C. and Branco, M. B.</b>,
 <i class='BibTitle'>Irreducible numerical semigroups</i>,
 <span class='BibJournal'>Pacific J. Math.</span>,
 <em class='BibVolume'>209</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2003</span>),
 <span class='BibPages'>131--143</span>.
</p>


<p><a id="biBR-GS" name="biBR-GS"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RG98</span>]   <b class='BibAuthor'>Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.</b>,
<a href="http://www.sciencedirect.com/science/article/pii/S0024379597003091"><i class='BibTitle'>Nonnegative elements of subgroups of \(\mathbbZ^n\)</i></a>,
 <span class='BibJournal'>Linear Algebra and its Applications </span>,
 <em class='BibVolume'>270</em> (<span class='BibNumber'>1-3</span>)
 (<span class='BibYear'>1998</span>),
 <span class='BibPages'>351357</span><br />
(<span class='BibNote'></span>).
</p>


<p><a id="biBMR1678508" name="biBMR1678508"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1678508">RG99a</a></span>]   <b class='BibAuthor'>Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.</b>,
<a href="https://doi.org/10.1007/BF03325435"><i class='BibTitle'>On free affine semigroups</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>58</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>1999</span>),
 <span class='BibPages'>367--385</span>.
</p>


<p><a id="biBRGS99" name="biBRGS99"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RG99b</span>]   <b class='BibAuthor'>Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.</b>,
 <i class='BibTitle'>Finitely generated commutative monoids</i>,
 <span class='BibPublisher'>Nova Science Publishers</span>,
 <span class='BibAddress'>New York</span>
 (<span class='BibYear'>1999</span>).
</p>


<p><a id="biBfgcm" name="biBfgcm"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=1694173">RG99c</a></span>]   <b class='BibAuthor'>Rosales, J. C. and Garc\'{\i}a-S\'{a}nchez, P. A.</b>,
 <i class='BibTitle'>Finitely generated commutative monoids</i>,
 <span class='BibPublisher'>Nova Science Publishers, Inc., Commack, NY</span>
 (<span class='BibYear'>1999</span>),
 <span class='BibPages'>xiv+185 pages</span>.
</p>


<p><a id="biBRGS04" name="biBRGS04"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RG04</span>]   <b class='BibAuthor'>Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.</b>,
 <i class='BibTitle'>Every positive integer is the Frobenius number
  of an irreducible numerical semigroup with at most four generators</i>,
 <span class='BibJournal'>Ark. Mat.</span>,
 <em class='BibVolume'>42</em>
 (<span class='BibYear'>2004</span>),
 <span class='BibPages'>301-306</span>.
</p>


<p><a id="biBRGbook" name="biBRGbook"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RG09</span>]   <b class='BibAuthor'>Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.</b>,
 <i class='BibTitle'>Numerical Semigroups</i>,
 <span class='BibPublisher'>Springer</span>
 (<span class='BibYear'>2009</span>).
</p>


<p><a id="biBMR3169635" name="biBMR3169635"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3169635">RG14</a></span>]   <b class='BibAuthor'>Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A.</b>,
<a href="https://doi.org/10.1080/00927872.2012.740117"><i class='BibTitle'>Constructing almost symmetric numerical semigroups from
              irreducible numerical semigroups</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
 <em class='BibVolume'>42</em> (<span class='BibNumber'>3</span>)
 (<span class='BibYear'>2014</span>),
 <span class='BibPages'>1362--1367</span>.
</p>


<p><a id="biBRGGB03" name="biBRGGB03"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RGGB03</span>]   <b class='BibAuthor'>Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.</b>,
 <i class='BibTitle'>Numerical semigroups with maximal embedding dimension</i>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>2</em>
 (<span class='BibYear'>2003</span>),
 <span class='BibPages'>47--53</span>.
</p>


<p><a id="biBRGGB04" name="biBRGGB04"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RGGB04</span>]   <b class='BibAuthor'>Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B.</b>,
 <i class='BibTitle'>Arf numerical semigroups</i>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>276</em>
 (<span class='BibYear'>2004</span>),
 <span class='BibPages'>3--12</span>.
</p>


<p><a id="biBRGGJ03" name="biBRGGJ03"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RGGJ03</span>]   <b class='BibAuthor'>Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'enez-Madrid, J. A.</b>,
 <i class='BibTitle'>The oversemigroups of a numerical semigroup</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>67</em>
 (<span class='BibYear'>2003</span>),
 <span class='BibPages'>145-158</span>.
</p>


<p><a id="biBRGSGGJM" name="biBRGSGGJM"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2038577">RGGJM04</a></span>]   <b class='BibAuthor'>Rosales, J. C., Garc\'{\i}a-S\'{a}nchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'{e}nez Madrid, J. A.</b>,
<a href="https://doi.org/10.1016/j.jpaa.2003.10.024"><i class='BibTitle'>Fundamental gaps in numerical semigroups</i></a>,
 <span class='BibJournal'>J. Pure Appl. Algebra</span>,
 <em class='BibVolume'>189</em> (<span class='BibNumber'>1-3</span>)
 (<span class='BibYear'>2004</span>),
 <span class='BibPages'>301--313</span>.
</p>


<p><a id="biBRGSUB" name="biBRGSUB"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2218353">RGU05</a></span>]   <b class='BibAuthor'>Rosales, J. C., Garc\'{\i}a-S\'{a}nchez, P. A. and Urbano-Blanco, J. M.</b>,
<a href="https://doi.org/10.2140/pjm.2005.218.379"><i class='BibTitle'>Modular Diophantine inequalities and numerical
      semigroups</i></a>,
 <span class='BibJournal'>Pacific J. Math.</span>,
 <em class='BibVolume'>218</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2005</span>),
 <span class='BibPages'>379--398</span>.
</p>


<p><a id="biBRos96" name="biBRos96"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Ros96a</span>]   <b class='BibAuthor'>Rosales, J. C.</b>,
 <i class='BibTitle'>An algorithmic method to compute a minimal relation for any numerical
      semigroup</i>,
 <span class='BibJournal'>Internat. J. Algebra Comput.</span>,
 <em class='BibVolume'>6</em>
 (<span class='BibYear'>1996</span>),
 <span class='BibPages'>441-455</span>.
</p>


<p><a id="biBR96" name="biBR96"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Ros96b</span>]   <b class='BibAuthor'>Rosales, J. C.</b>,
 <i class='BibTitle'>On numerical semigroups</i>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>52</em>
 (<span class='BibYear'>1996</span>),
 <span class='BibPages'>307-318</span>.
</p>


<p><a id="biBR07" name="biBR07"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2316425">Ros07</a></span>]   <b class='BibAuthor'>Rosales, J. C.</b>,
<a href="https://doi.org/10.1142/S0219498807002223"><i class='BibTitle'>Subadditive periodic functions and numerical semigroups</i></a>,
 <span class='BibJournal'>J. Algebra Appl.</span>,
 <em class='BibVolume'>6</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2007</span>),
 <span class='BibPages'>305--313</span>.
</p>


<p><a id="biBRoune" name="biBRoune"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2381966">Rou08</a></span>]   <b class='BibAuthor'>Roune, B. H.</b>,
<a href="https://doi.org/10.1016/j.jsc.2007.06.002"><i class='BibTitle'>Solving thousand-digit Frobenius problems using
      Gr\"obner
              bases</i></a>,
 <span class='BibJournal'>J. Symbolic Comput.</span>,
 <em class='BibVolume'>43</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>1--7</span>.
</p>


<p><a id="biBRUB" name="biBRUB"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2271340">RU06</a></span>]   <b class='BibAuthor'>Rosales, J. C. and Urbano-Blanco, J. M.</b>,
<a href="https://doi.org/10.1016/j.jalgebra.2006.08.009"><i class='BibTitle'>Opened modular numerical semigroups</i></a>,
 <span class='BibJournal'>J. Algebra</span>,
 <em class='BibVolume'>306</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2006</span>),
 <span class='BibPages'>368--377</span>.
</p>


<p><a id="biBRosalesVasco2008MIA" name="biBRosalesVasco2008MIA"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2410272">RV08</a></span>]   <b class='BibAuthor'>Rosales, J. C. and Vasco, P.</b>,
<a href="https://doi.org/10.7153/mia-11-14"><i class='BibTitle'>The smallest positive integer that is solution of a
              proportionally modular Diophantine inequality</i></a>,
 <span class='BibJournal'>Math. Inequal. Appl.</span>,
 <em class='BibVolume'>11</em> (<span class='BibNumber'>2</span>)
 (<span class='BibYear'>2008</span>),
 <span class='BibPages'>203--212</span>.
</p>


<p><a id="biBMR3354072" name="biBMR3354072"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3354072">Spi15</a></span>]   <b class='BibAuthor'>Spirito, D.</b>,
<a href="https://doi.org/10.1080/00927872.2014.908201"><i class='BibTitle'>Star operations on numerical semigroups</i></a>,
 <span class='BibJournal'>Comm. Algebra</span>,
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 (<span class='BibYear'>2015</span>),
 <span class='BibPages'>2943--2963</span>.
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<p><a id="biBStokes" name="biBStokes"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3528435">Sto16</a></span>]   <b class='BibAuthor'>Stokes, K.</b>,
<a href="https://doi.org/10.1007/s00233-015-9741-1"><i class='BibTitle'>Patterns of ideals of numerical semigroups</i></a>,
 <span class='BibJournal'>Semigroup Forum</span>,
 <em class='BibVolume'>93</em> (<span class='BibNumber'>1</span>)
 (<span class='BibYear'>2016</span>),
 <span class='BibPages'>180--200</span>.
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<p><a id="biBSUER" name="biBSUER"></a></p>
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[<span class='BibKey'>Süe22</span>]   <b class='BibAuthor'>Süer, M.</b>,
<a href="https://arxiv.org/abs/2207.13206"><i class='BibTitle'>Irreducibility of Arf Numerical Semigroups</i></a>,
 <span class='BibPublisher'>arXiv</span>
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<p><a id="biBSzW" name="biBSzW"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=900339">SW86</a></span>]   <b class='BibAuthor'>Sz{\'e}kely, L. A. and Wormald, N. C.</b>,
 <i class='BibTitle'>Generating functions for the Frobenius problem with
      \(2\)
              and \(3\) generators</i>,
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 <em class='BibVolume'>15</em>
 (<span class='BibYear'>1986</span>),
 <span class='BibPages'>49--57</span>.
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<p><a id="biB4ti2" name="biB4ti2"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>tt</span>]   <b class='BibAuthor'>4ti2 team,</b>,
 <i class='BibTitle'>4ti2---A software package for algebraic, geometric and
              combinatorial problems on linear spaces</i>,
<span class='BibHowpublished'>{A}vailable at www.4ti2.de</span>.
</p>


<p><a id="biBG-I-K-T" name="biBG-I-K-T"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>tttt17</span>]   <b class='BibAuthor'>{Goto}, S., {Isobe}, R., {Kumashiro}, S. and {Taniguchi}, N.</b>,
 <i class='BibTitle'>Characterization of generalized Gorenstein rings</i>,
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<p><a id="biBUgolini" name="biBUgolini"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=3611782">Ugo17</a></span>]   <b class='BibAuthor'>Ugolini, S.</b>,
<a href="https://doi.org/10.5486/PMD.2017.7500"><i class='BibTitle'>On numerical semigroups closed with respect to the action of
              affine maps</i></a>,
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<p><a id="biBWilf" name="biBWilf"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=0556658">Wil78</a></span>]   <b class='BibAuthor'>Wilf, H. S.</b>,
 <i class='BibTitle'>A circle-of-lights algorithm for the ``money-changing
              problem''</i>,
 <span class='BibJournal'>Amer. Math. Monthly</span>,
 <em class='BibVolume'>85</em> (<span class='BibNumber'>7</span>)
 (<span class='BibYear'>1978</span>),
 <span class='BibPages'>562--565</span>.
</p>


<p><a id="biBZ86" name="biBZ86"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Zar86</span>]   <b class='BibAuthor'>Zariski, O.</b>,
 <i class='BibTitle'>Le probl\`eme des modules pour les courbes planes</i>,
 <span class='BibPublisher'>Hermann</span>
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</p>

<p> </p>


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