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<h3>References</h3>

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[ADG20] Assi, A., D'Anna, M. and Garc\'{\i}a-S\'{a}nchez, P. A.,
<a href="https://doi.org/10.1007/978-3-030-54943-5">Numerical semigroups and applications</a>,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2729387">AG10</a>] Aguil{\'o}-Gost, F. and Garc{\'{\i}}a-S{\'a}nchez, P. A.,
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[AG13] Assi, A. and Garc\'{\i}a-S\'anchez, P. A.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=3558713">AG16b</a>] Assi, A. and Garc\'{\i}a-S\'{a}nchez, P. A.,
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[BDF97] Barucci, V., Dobbs, D. D. and Fontana, M.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1747441">BDF00a</a>] Barucci, V., D'Anna, M. and Fr\"{o}berg, R.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=1767576">BDF00b</a>] Barucci, V., D'Anna, M. and Fr\"{o}berg, R.,
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[BF97] Barucci, V. and Fr\"oberg, R.,
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[BF06] Barucci, V. and Fr\"oberg, R.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2214415">BG06</a>] Bras-Amor{\'o}s, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.,
<a href="https://doi.org/10.1016/j.laa.2005.11.007">Patterns on numerical semigroups</a>,
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[BGG11] Blanco, V., Garc\'{\i}a-S\'anchez, P. A. and Geroldinger, A.,
Semigroup-theoretical characterizations of arithmetical invariants
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[<a href="https://www.ams.org/mathscinet-getitem?mr=3053780">BH13</a>] Bryant, L. and Hamblin, J.,
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[BIRC14] Bruns, W., Ichim, B., R\"omer, T. and C., S.,
Normaliz. Algorithms for rational cones and affine monoids
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[<a href="https://www.ams.org/mathscinet-getitem?mr=3647965">BOP17</a>] Barron, T., O'Neill, C. and Pelayo, R.,
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[BOR18] Branco, M., Ojeda, I. and Rosales, J. C.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=4301804">BOR21</a>] Branco, M. B., Ojeda, I. and Rosales, J. C.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2476582">BR09</a>] Bullejos, M. and Rosales, J. C.,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=3199729">BR13</a>] Blanco, V. and Rosales, J. C.,
<a href="https://doi.org/10.1515/form.2011.151">The tree of irreducible numerical semigroups with fixed
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<a id="biBBr-acute" name="biBBr-acute"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2094884">Bra04</a>] Bras-Amor\'os, M.,
<a href="https://doi.org/10.1109/TIT.2004.828104">Acute semigroups, the order bound on the minimum distance, and
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<a id="biBB-A08" name="biBB-A08"></a>

[Bra08] Bras-Amor\'os, M.,
Fibonacci-like behavior of the number of numerical semigroups of
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<a id="biBbras-ns-codes" name="biBbras-ns-codes"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3288285">Bra13</a>] Bras-Amor\'{o}s, M.,
<a href="https://doi.org/10.1142/9789814335768_0005">Numerical semigroups and codes</a>,
 in Algebraic geometry modeling in information theory,
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[<a href="https://www.ams.org/mathscinet-getitem?mr=2675524">Bry10</a>] Bryant, L.,
<a href="https://doi.org/10.1080/00927870903025993">Goto numbers of a numerical semigroup ring and the
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Comm. Algebra,
38 (6)
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<a id="biBdilatation" name="biBdilatation"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3917961">BS19</a>] Barucci, V. and Strazzanti, F.,
<a href="https://doi.org/10.1007/s00233-018-9922-9">Dilatations of numerical semigroups</a>,
Semigroup Forum,
98 (2)
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<a id="biBR-GS-GG-B" name="biBR-GS-GG-B"></a>

[CAGB02] C., R., Garc\'{\i}a-S\'anchezP. A., Garc\'{\i}a-Garc\'{\i}a, J. I., and Branco, M. B.,
<a href="http://journals.cambridge.org/article_S0024610701003052">SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS</a>,
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[CBJZA13] Cortadellas Ben\'{\i}tez, T., Jafari, R. and Zarzuela Armengou, S.,
On teh Ap\'ery sets of monomial curves,
Semigroup Forum,
86
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[<a href="https://www.ams.org/mathscinet-getitem?mr=MR1283022">CD94</a>] Contejean, E. and Devie, H.,
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<a id="biBSingularpackage" name="biBSingularpackage"></a>

[CdG12] Costantini, M. and de Graaf, W.,
GAP package singular; the GAP interface to Singular
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<a id="biBC-F-U" name="biBC-F-U"></a>

[CFR18] Cisto, C., Failla, G. and R., U.,
On the generators of a generalized numerical semigroup,
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<a id="biBCGL" name="biBCGL"></a>

[CGD07] Chapman, S. T., Garc\'{\i}a-S\'anchez, P. A. and D., L.,
The catenary and tame degree of numerical semigroups,
Forum Math.
(2007),
1--13.


<a id="biBC-GS-HP-M" name="biBC-GS-HP-M"></a>

[CGHM19] Ciolan, E.-A., Garc\'{i}a-S\'{a}nchez, P. A., Herrera-Poyatos, A. and Moree, P.,
Cyclotomic exponent sequences of numerical semigroups,
preprint
(2019).


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

[CGL+06] Chapman, S. T., Garc\'{\i}a-S\'anchez, P. A., Llena, D., Ponomarenko, V. and Rosales, J. C.,
The catenary and tame degree in finitely generated commutative
 cancellative
monoids,
Manuscripta Math.,
120 (3)
(2006),
253--264.


<a id="biBC-GS-M" name="biBC-GS-M"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3483156">CGM16</a>] Ciolan, E.-A., Garc\'{i}a-S\'{a}nchez, P. A. and Moree, P.,
<a href="https://doi.org/10.1137/140989479">Cyclotomic numerical semigroups</a>,
SIAM J. Discrete Math.,
30 (2)
(2016),
650--668.


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[CHM06] Chapman, S. T., Holden, M. T. and Moore, T. A.,
Full elasticity in atomic monoids and integral domains,
Rocky Mountain J. Math.,
36 (5)
(2006),
1437--1455.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=3110597">CRA13</a>] Chappelon, J. and Ram{\'{\i}}rez Alfons{\'{\i}}n, J. L.,
<a href="https://doi.org/10.1007/s00233-012-9458-3">On the M\"obius function of the locally finite poset
 associated with a numerical semigroup</a>,
Semigroup Forum,
87 (2)
(2013),
313--330.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=949819">DdlM88</a>] Delgado de la Mata, F.,
<a href="https://doi.org/10.1007/BF01258440">Gorenstein curves and symmetry of the semigroup of values</a>,
Manuscripta Math.,
61 (3)
(1988),
285--296.


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[<a href="https://www.ams.org/mathscinet-getitem?mr=3493240">DG16</a>] Delgado, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A.,
numericalsgps, a GAP package for numerical
 semigroups,
ACM Commun. Comput. Algebra,
50 (1)
(2016),
12--24.


<a id="biBDA-G-H" name="biBDA-G-H"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1842007">DGH01</a>] D'Anna, M., Guerrieri, A. and Heinzer, W.,
<a href="https://doi.org/10.1081/AGB-100001550">Invariants of ideals having principal reductions</a>,
Comm. Algebra,
29 (2)
(2001),
889--906.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=2325970">DGM06</a>] Delgado, M., Garc\'{\i}a-S\'anchez, P. A. and Morais, J.,
On the GAP package numericalsgps,
 in Fifth Conference on Discrete Mathematics and
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Univ. Valladolid,
Ciencias (Valladolid),
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(2006),
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<a id="biBDGSM" name="biBDGSM"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=3786416">DGMT18</a>] D'Anna, M., Garc\'{\i}a-S\'{a}nchez, P. A., Micale, V. and Tozzo, L.,
<a href="https://doi.org/10.1142/S0218196718500091">Good subsemigroups of Bbb N^n</a>,
Internat. J. Algebra Comput.,
28 (2)
(2018),
179--206.


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

[DGPS12] Decker, W., Greuel, G.-M., Pfister, G. and Sch\"onemann, H.,
\sc Singular 3-1-6 --- A computer algebra system
 for polynomial computations
(2012),
\url{https://www.singular.uni-kl.de}.


<a id="biBDGSRP15" name="biBDGSRP15"></a>

[DGR16] Delgado, M., Garc{\'{\i}}a-S{\'a}nchez, P. A. and Robles-P{\'e}rez, A. M.,
Numerical semigroups with a given set of pseudo-Frobenius
 numbers,
LMS J. Comput. Math.,
19
(2016),
186--205.


<a id="biBDA-M-S" name="biBDA-M-S"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2813470">DMS11</a>] D'Anna, M., Micale, V. and Sammartano, A.,
On the associated graded ring of a semigroup ring,
J. Commut. Algebra,
3 (2)
(2011),
147--168.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=3010100">DMS13</a>] D'Anna, M., Micale, V. and Sammartano, A.,
<a href="https://doi.org/10.1016/j.jpaa.2012.09.024">When the associated graded ring of a semigroup ring is
 complete intersection</a>,
J. Pure Appl. Algebra,
217 (6)
(2013),
1007--1017.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=3189106">DMS14</a>] D'Anna, M., Micale, V. and Sammartano, A.,
<a href="https://doi.org/10.1007/s00233-013-9547-y">Classes of complete intersection numerical semigroups</a>,
Semigroup Forum,
88 (2)
(2014),
453--467.


<a id="biBDA-M-M" name="biBDA-M-M"></a>

[DMV09] D'Anna, M., Mezzasalma, M. and V., M.,
On the Buchsbaumness of the associated graded ring of a
 one-dimensional local ring,
Comm. Algebra,
37
(2009),
1594--1603.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=3079777">DS13</a>] D'Anna, M. and Strazzanti, F.,
<a href="https://doi.org/10.1007/s00233-012-9451-x">The numerical duplication of a numerical semigroup</a>,
Semigroup Forum,
87 (1)
(2013),
149--160.


<a id="biBgas-semigroups" name="biBgas-semigroups"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=4283166">DS21</a>] D'Anna, M. and Strazzanti, F.,
<a href="https://doi.org/10.1080/00927872.2021.1900213">Almost canonical ideals and GAS numerical semigroups</a>,
Comm. Algebra,
49 (8)
(2021),
3534--3551.


<a id="biBE01" name="biBE01"></a>

[Eli01] Elias, J.,
On the deep structure of the blowing-up of curve
 singularities,
Math. Proc. Camb. Phil. Soc.,
131
(2001),
227--240.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=3836842">Eli18</a>] Eliahou, S.,
<a href="https://doi.org/10.4171/JEMS/807">Wilf's conjecture and Macaulay's theorem</a>,
J. Eur. Math. Soc. (JEMS),
20 (9)
(2018),
2105--2129.


<a id="biBMR1394747" name="biBMR1394747"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1394747">ES96</a>] Eisenbud, D. and Sturmfels, B.,
<a href="https://doi.org/10.1215/S0012-7094-96-08401-X">Binomial ideals</a>,
Duke Math. J.,
84 (1)
(1996),
1--45.


<a id="biBFGH87" name="biBFGH87"></a>

[FGR87] Fr\"oberg, R., Gottlieb, C. and R., H.,
On numerical semigroups,
Semigroup Forum,
35 (1)
(1987),
63--83.


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

[GH06] Geroldinger, A. and Halter-Koch, F.,
Non-unique Factorizations: Algebraic, Combinatorial and
Analytic Theory,
Chapman \& Hall/CRC
(2006).


<a id="biBarf-frob-gen" name="biBarf-frob-gen"></a>

[GHKR17] Garc{\'{\i}}a-S{\'a}nchez, P. A., Heredia, B. A., Karakas, H. I. and Rosales, J. C.,
Parametrizing Arf numerical semigroups,
J. Algebra Appl.,
16
(2017),
1750209 (31 pages).


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

[GHS14] Gutsche, S., Horn, M. and S\"oger, C.,
NormalizInterface for GAP
(2014),
\url{https://github.com/gap-packages/NormalizInterface}.


<a id="biBGG-MF-VT" name="biBGG-MF-VT"></a>

[GMV15] Garc\'{\i}a-Garc\'{\i}a, J. I., Moreno-Fr\'{\i}as, M. A. and Vigneron-Tenorio, A.,
Computation of Delta sets of numerical monoids,
Monatsh. Math. ,
178
(2015),
457--472.


<a id="biBGS-O" name="biBGS-O"></a>

[GO10] Garc\'{\i}a-S\'anchez, P. A. and Ojeda, I.,
Uniquely presented finitely generated commutative monoids,
Pacific J. Math.,
249
(2010),
91--105.


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

[<a href="https://www.ams.org/mathscinet-getitem?mr=3910672">GOW19</a>] Garc\'{\i}a-S\'{a}nchez, P. A., O'Neill, C. and Webb, G.,
<a href="https://doi.org/10.1142/S0219498819500191">The computation of factorization invariants for affine
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