[AAGS17] Abbas, A., Assi, A. and García-Sánchez, P. A., Canonical bases of modules over one dimensional k-algebras, arxiv:1703.02825 (2017).
[AGGS10] Aguil{\'o}-Gost, F. and Garc{\'{\i}}a-S{\'a}nchez, P. A., Factoring in embedding dimension three numerical semigroups, Electron. J. Combin., 17 (1) (2010), Research Paper 138, 21.
[AGS13] Assi, A. and Garc\'{\i}a-S\'anchez, P. A., Constructing the set of complete intersection numerical semigroups with a given Frobenius number, Applicable Algebra in Engineering, Communication and Computing (2013).
[AGS16] Assi, A. and Garc\'{\i}a-S\'anchez, P. A., Algorithms for curves with one place at infinity, Journal of Symbolic Computation, 74 (2016), 475--492.
[AGSM17] Assi, A., Garc\'{\i}a-S\'anchez, P. A. and Micale, V., Bases of subalgebras of K[[x]] and K[x], Journal of Symbolic Computation, 79 (2017), 4--22.
[BA04] Bras-Amor\'os, M., Acute semigroups, the order bound on the minimum distance, and the Feng-Rao improvements, IEEE Trans. Inform. Theory, 50 (6) (2004), 1282--1289.
[BA08] Bras-Amor\'os, M., Fibonacci-like behavior of the number of numerical semigroups of a given genus, Semigroup Forum, 76 (2008), 379--384.
[BAGS06] Bras-Amor{\'o}s, M. and Garc{\'{\i}}a-S{\'a}nchez, P. A., Patterns on numerical semigroups, Linear Algebra Appl., 414 (2-3) (2006), 652--669.
[BC77] Bertin, J. and Carbonne, P., Semi-groupes d'entiers et application aux branches, J. Algebra, 49 (1) (1977), 81--95.
[BD89] Bradford, R. J. and Davenport, J. H., Effective tests for cyclotomic polynomials, in Symbolic and algebraic computation (Rome, 1988), Springer, Berlin, Lecture Notes in Comput. Sci., 358 (1989), 244--251.
[BDF97] Barucci, V., Dobbs, D. D. and Fontana, M., Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, American Mathematical Society, Memoirs of the American Mathematical Society (598) (1997).
[BF06] Barucci, V. and Fr\"oberg, R., Associated graded rings of one-dimensional analytically irreducible rings, J. Algebra, 304 (2006), 349--358.
[BGJ+14] Barakat, M., Gutsche, S., Jambor, S., Lange-Hegermann, M., Lorenz, A. and Motsak, O.,
GradedModules, A homalg based package for the Abelian
category of finitely presented graded modules over
computable graded rings, Version 2014.09.17
(2014)
(GAP package),
\href
{http://homalg.math.rwth-aachen.de/~barakat/homalg-project/Gr\
adedModules/}
{\texttt{http://homalg.math.rwth-aachen.de/}\discretionary
{}{}{}\texttt{\texttt{\symbol{126}}barakat/}\discretionary
{}{}{}\texttt{homalg-project/}\discretionary
{}{}{}\texttt{GradedModules/}}.
[BGSG11] Blanco, V., Garc\'{\i}a-S\'anchez, P. A. and Geroldinger, A., Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids, Illinois J. Math., 55 (2011), 1385--1414.
[BH13] Bryant, L. and Hamblin, J., The maximal denumerant of a numerical semigroup, Semigroup Forum, 86 (3) (2013), 571--582.
[BIRC14] Bruns, W., Ichim, B., R\"omer, T. and C., S., Normaliz. Algorithms for rational cones and affine monoids (2014), \url{http://www.math.uos.de/normaliz}.
[BOP14] Barron, T., O'Neill, C. and Pelayo, R., On the computation of delta sets and \(\omega\)-primality in numerical monoids, preprint (2014).
[BR97] Barucci, V. and R., F., One-dimensional almost Gorenstein Rings, J. Algebra, 188 (1997), 418--442.
[BR09] Bullejos, M. and Rosales, J. C., Proportionally modular Diophantine inequalities and the Stern-Brocot tree, Math. Comp., 78 (266) (2009), 1211--1226.
[BR13] Blanco, V. and Rosales, J. C., The tree of irreducible numerical semigroups with fixed Frobenius number, Forum Math., 25 (6) (2013), 1249--1261.
[Bry10] Bryant, L., Goto numbers of a numerical semigroup ring and the Gorensteiness of associated graded rings, Comm. Algebra, 38 (6) (2010), 2092--2128.
[CAGGB02] C., R., Garc\'{\i}a-S\'anchezP. A., Garc\'{\i}a-Garc\'{\i}a, J. I., and Branco, M. B., SYSTEMS OF INEQUALITIES AND NUMERICAL SEMIGROUPS, Journal of the London Mathematical Society, 65 (2002), 611--623.
[CBJZA13] Cortadellas Ben\'{\i}tez, T., Jafari, R. and Zarzuela Armengou, S., On teh Ap\'ery sets of monomial curves, Semigroup Forum, 86 (2013), 289--320.
[CD94] Contejean, E. and Devie, H., An efficient incremental algorithm for solving systems of linear Diophantine equations, Inform. and Comput., 113 (1) (1994), 143--172.
[CdG12] Costantini, M. and de Graaf, W., GAP package singular; the GAP interface to Singular (2012), \url{http://gap-system.org/Packages/singular.html}.
[CGSD07] 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.
[CGSL+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.
[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.
[CRA13] Chappelon, J. and Ram{\'{\i}}rez Alfons{\'{\i}}n, J. L., On the M\"obius function of the locally finite poset associated with a numerical semigroup, Semigroup Forum, 87 (2) (2013), 313--330.
[DGH01] D'Anna, M., Guerrieri, A. and Heinzer, W., Invariants of ideals having principal reductions, Comm. Algebra, 29 (2) (2001), 889--906.
[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{http://www.singular.uni-kl.de}.
[DGS16] 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.
[DGSM06] Delgado, M., Garc\'{\i}a-S\'anchez, P. A. and Morais, J., On the GAP package numericalsgps, in Fifth Conference on Discrete Mathematics and Computer Science (Spanish), Univ. Valladolid, Ciencias (Valladolid), 23, Secr. Publ. Intercamb. Ed., Valladolid (2006), 271--278.
[DGSM16] D'Anna, M., Garc{\'{\i}}a-S{\'a}nchez, P. A. and Micale, E., Good semigroups, preprint (2016).
[DGSRP16] 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.
[DMS11] 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.
[DMS13] D'Anna, M., Micale, V. and Sammartano, A., When the associated graded ring of a semigroup ring is complete intersection, J. Pure Appl. Algebra, 217 (6) (2013), 1007--1017.
[DMS14] D'Anna, M., Micale, V. and Sammartano, A., Classes of complete intersection numerical semigroups, Semigroup Forum, 88 (2) (2014), 453--467.
[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.
[DS13] D'Anna, M. and Strazzanti, F., The numerical duplication of a numerical semigroup, Semigroup Forum, 87 (1) (2013), 149--160.
[Eli01] Elias, J., On the deep structure of the blowing-up of curve singularities, Math. Proc. Camb. Phil. Soc., 131 (2001), 227--240.
[Eli15] Eliahou, S., Wilf's conjecture and Macaulay's theorem, preprint (2015).
[ES96] Eisenbud, D. and Sturmfels, B., Binomial ideals, Duke Math. J., 84 (1) (1996), 1--45.
[FGR87] Fr\"oberg, R., Gottlieb, C. and R., H., On numerical semigroups, Semigroup Forum, 35 (1) (1987), 63--83.
[GGMFVT15] 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.
[GHK06] Geroldinger, A. and Halter-Koch, F., Non-unique Factorizations: Algebraic, Combinatorial and Analytic Theory, Chapman \& Hall/CRC (2006).
[GHS14] Gutsche, S., Horn, M. and S\"oger, C., NormalizInterface for GAP (2014), \url{https://github.com/fingolfin/NormalizInterface}.
[GSHKR17] 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).
[GSO10] Garc\'{\i}a-S\'anchez, P. A. and Ojeda, I., Uniquely presented finitely generated commutative monoids, Pacific J. Math., 249 (2010), 91--105.
[GSOSRN13] Garc{\'{\i}}a S{\'a}nchez, P. A., Ojeda, I. and S{\'a}nchez-R. -Navarro, A., Factorization invariants in half-factorial affine semigroups, Internat. J. Algebra Comput., 23 (1) (2013), 111--122.
[GSOW17] Garc\'{\i}a-S\'anchez, P. A., O'Neill, C. and Webb, G., On the computation of factorization invariants for affine semigroups, arxiv:1504.02998 (2017).
[Gut] Gutsche, S., 4ti2Interface, A link to 4ti2, \url{http://www.gap-system.org/Packages/4ti2interface.html}.
[Her70] Herzog, J., Generators and relations of abelian semigroups and semigroup rings. , Manuscripta Math., 3 (1970), 175--193.
[HS04] Herzinger, K. and Sanford, R., Minimal Generating Sets for Relative Ideals in Numerical Semigroups of Multiplicity Eight, Communications in Algebra, 32 (12) (2004), 4713-4731.
[KP95] Kirfel, C. and Pellikaan, R.,
The minimum distance of codes in an array coming from
telescopic semigroups,
IEEE Trans. Inform. Theory,
41 (6, part 1)
(1995),
1720--1732
(Special issue on algebraic geometry codes).
[KW14] Kunz, E. and Waldi, R., Geometrical illustration of numerical semigroups and of some of their invariants, Semigroup Forum, 89 (3) (2014), 664--691.
[MCOT15] M{\'a}rquez-Campos, G., Ojeda, I. and Tornero, J. M., On the computation of the Ap\'ery set of numerical monoids and affine semigroups, Semigroup Forum, 91 (1) (2015), 139--158.
[Mic02] Micale, V., On monomial semigroups, Communications in Algebra, 30 (2002), 4687 - 4698.
[Mor14] Moree, P., Numerical semigroups, cyclotomic polynomials, and Bernoulli numbers, Amer. Math. Monthly, 121 (10) (2014), 890--902.
[Phi10] Philipp, A., A characterization of arithmetical invariants by the monoid of relations, Semigroup Forum, 81 (2010), 424--434.
[RB03] Rosales, J. C. and Branco, M. B., Irreducible numerical semigroups, Pacific J. Math., 209 (1) (2003), 131--143.
[RGS98] Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A.,
Nonnegative elements of subgroups of \(\mathbbZ^n\),
Linear Algebra and its Applications ,
270 (1-3)
(1998),
351- 357
().
[RGS99a] Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A., On free affine semigroups, Semigroup Forum, 58 (3) (1999), 367--385.
[RGS99b] Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A., Finitely generated commutative monoids, Nova Science Publishers, New York (1999).
[RGS04] Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A., Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators, Ark. Mat., 42 (2004), 301-306.
[RGS09] Rosales, J. C. and Garc\'{\i}a-S\'anchez, P. A., Numerical Semigroups, Springer (2009).
[RGS14] Rosales, J. C. and Garc{\'{\i}}a-S{\'a}nchez, P. A., Constructing almost symmetric numerical semigroups from irreducible numerical semigroups, Comm. Algebra, 42 (3) (2014), 1362--1367.
[RGSGGB03] Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B., Numerical semigroups with maximal embedding dimension, J. Algebra, 2 (2003), 47--53.
[RGSGGB04] Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Branco, M. B., Arf numerical semigroups, J. Algebra, 276 (2004), 3--12.
[RGSGGJM03] Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'enez-Madrid, J. A., The oversemigroups of a numerical semigroup, Semigroup Forum, 67 (2003), 145-158.
[RGSGGJM04] Rosales, J. C., Garc\'{\i}a-S\'anchez, P. A., Garc\'{\i}a-Garc\'{\i}a, J. I. and Jim\'enez Madrid, J. A., Fundamental gaps in numerical semigroups, J. Pure Appl. Algebra, 189 (1-3) (2004), 301--313.
[Ros96a] Rosales, J. C., An algorithmic method to compute a minimal relation for any numerical semigroup, Internat. J. Algebra Comput., 6 (1996), 441-455.
[Ros96b] Rosales, J. C., On numerical semigroups, Semigroup Forum, 52 (1996), 307-318.
[Rou08] Roune, B. H., Solving thousand-digit Frobenius problems using Gr\"obner bases, J. Symbolic Comput., 43 (1) (2008), 1--7.
[Spi15] Spirito, D., Star operations on numerical semigroups, Comm. Algebra, 43 (7) (2015), 2943--2963.
[Sto15] Stokes, K., Patterns of ideals of numerical semigroups, preprint (2015).
[SW86] Sz{\'e}kely, L. A. and Wormald, N. C., Generating functions for the Frobenius problem with \(2\) and \(3\) generators, Math. Chronicle, 15 (1986), 49--57.
[tt] 4ti2 team,, 4ti2---A software package for algebraic, geometric and combinatorial problems on linear spaces, {A}vailable at www.4ti2.de.
[Ugo16] Ugolini, S., On numerical semigroups closed with respect to the action of affine maps, arXiv, 1505.06580 (2016).
[Wil78] Wilf, H. S., A circle-of-lights algorithm for the ``money-changing problem'', Amer. Math. Monthly, 85 (7) (1978), 562--565.
[Zar86] Zariski, O., Le probl\`eme des modules pour les courbes planes, Hermann (1986).
generated by GAPDoc2HTML