Publications

2018
García-Sánchez PA, Llena D, Moscariello A. Delta sets for nonsymmetric numerical semigroups with embedding dimension three. Forum Math.. 2018;30:15-30.
2017
Assi A, García-Sánchez PA, Micale V.. Bases of subalgebras of $\BbbK[\![x]\!]$ and $\BbbK[x]$. J. Symbolic Comput.. 2017;79:4-22.
García-Sánchez PA, Heredia B., Karakaş H., Rosales J.. Parametrizing Arf numerical semigroups. J. Algebra Appl.. 2017;16:1750209, 31.
García-Sánchez PA, Llena D., Moscariello A.. Delta sets for symmetric numerical semigroups with embedding dimension three. Aequationes Math.. 2017;91:579-600.
2016
Assi A, García-Sánchez PA. Numerical semigroups and applications. Vol 1 Springer, [Cham] 2016.
Delgado M., García-Sánchez PA. $\ssfnumericalsgps$, a $\ssfGAP$ package for numerical semigroups. ACM Commun. Comput. Algebra. 2016;50:12-24.
Ciolan E-, García-Sánchez PA, Moree P. Cyclotomic numerical semigroups. SIAM J. Discrete Math.. 2016;30:650-668.
Assi A, García-Sánchez PA. Algorithms for curves with one place at infinity. J. Symbolic Comput.. 2016;74:475-492.
Chapman S., García-Sánchez PA, Tripp Z., Viola C. Measuring primality in numerical semigroups with embedding dimension three. J. Algebra Appl.. 2016;15:1650007, 16.
Delgado M., García-Sánchez PA, Robles-Pérez A.. Numerical semigroups with a given set of pseudo-Frobenius numbers. LMS Journal of Computation and Mathematics. 2016;19(1):186-205.
2015
Assi A, García-Sánchez PA, Ojeda I. Frobenius vectors, Hilbert series and gluings of affine semigroups. J. Commut. Algebra. 2015;7:317-335.
Delgado M, García-Sánchez PA, Morais J. numericalsgps, an accepted GAP package 2015.
Farrán J., García-Sánchez PA. The second Feng-Rao number for codes coming from inductive semigroups. IEEE Trans. Inform. Theory. 2015;61:4938-4947.
Aguiló-Gost F, García-Sánchez PA, Llena D.. On the number of $\ssfL$-shapes in embedding dimension four numerical semigroups. Discrete Math.. 2015;338:2168-2178.
García-Sánchez PA, Viola C. When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three. Involve. 2015;8:677-694.
2014
Delgado M, Farrán J., García-Sánchez PA, Llena D. On the weight hierarchy of codes coming from semigroups with two generators. IEEE Trans. Inform. Theory. 2014;60:282-295.
Rosales J., García-Sánchez PA. Constructing almost symmetric numerical semigroups from irreducible numerical semigroups. Comm. Algebra. 2014;42:1362-1367.
Taha SA, García-Sánchez PA. Homogenization of a nonsymmetric embedding-dimension-three numerical semigroup. Involve. 2014;7:77-96.
2013
Assi A, García-Sánchez PA. Constructing the set of complete intersection numerical semigroups with a given Frobenius number. Appl. Algebra Engrg. Comm. Comput.. 2013;24:133-148.
Delgado M, García-Sánchez PA, Rosales JC. Numerical semigroups problem list 2013.
Delgado M., Farrán J., García-Sánchez PA, Llena D.. On the generalized Feng-Rao numbers of numerical semigroups generated by intervals. Math. Comp.. 2013;82:1813-1836.
Bras-Amorós M, García-Sánchez PA, Vico-Oton A. Nonhomogeneous patterns on numerical semigroups. Internat. J. Algebra Comput.. 2013;23:1469-1483.
García-Sánchez PA, Leamer M.. Huneke-Wiegand Conjecture for complete intersection numerical semigroup rings. J. Algebra. 2013;391:114-124.
2012
Chapman S., García-Sánchez PA, Llena D., Malyshev A., Steinberg D.. On the delta set and the Betti elements of a BF-monoid. Arab. J. Math. (Springer). 2012;1:53-61.
Bullejos M., García-Sánchez PA. Minimal presentations for monoids with the ascending chain condition on principal ideals. Semigroup Forum. 2012;85:185-190.
2011
Blanco V, García-Sánchez PA, Geroldinger A.. Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. Illinois J. Math.. 2011;55:1385-1414 (2013).
Blanco V, García-Sánchez PA, Puerto J. Counting numerical semigroups with short generating functions. Internat. J. Algebra Comput.. 2011;21:1217-1235.
Chapman S., García-Sánchez PA, Llena D., Marshall J.. Elements in a numerical semigroup with factorizations of the same length. Canad. Math. Bull.. 2011;54:39-43.
2010
García-Sánchez PA, Ojeda I. Uniquely presented finitely generated commutative monoids. Pacific J. Math.. 2010;248:91-105.
Aguiló-Gost F, García-Sánchez PA. Factoring in embedding dimension three numerical semigroups. Electron. J. Combin.. 2010;17:Research Paper 138, 21.
2009
Chapman S., García-Sánchez PA, Llena D.. The catenary and tame degree of numerical monoids. Forum Math.. 2009;21:117-129.
Rosales J., García-Sánchez PA. Numerical semigroups. Vol 20 Springer, New York 2009.
2008
García-Sánchez PA, Llena D., Rosales J.. Strongly taut finitely generated monoids. Monatsh. Math.. 2008;155:119-124.
Rosales J., García-Sánchez PA. Every numerical semigroup is one half of infinitely many symmetric numerical semigroups. Comm. Algebra. 2008;36:2910-2916.
Rosales J., García-Sánchez PA, Urbano-Blanco J.. The set of solutions of a proportionally modular Diophantine inequality. J. Number Theory. 2008;128:453-467.
Rosales J., García-Sánchez PA. Numerical semigroups having a Toms decomposition. Canad. Math. Bull.. 2008;51:134-139.
Rosales J., García-Sánchez PA. Every numerical semigroup is one half of a symmetric numerical semigroup. Proc. Amer. Math. Soc.. 2008;136:475-477 (electronic).
Delgado M., García-Sánchez PA, Rosales J., Urbano-Blanco J.. Systems of proportionally modular Diophantine inequalities. Semigroup Forum. 2008;76:469-488.
2006
García-Sánchez PA. Numerical semigroups mini-course 2006.
Chapman S., García-Sánchez PA, Llena D., Rosales J.. Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations. Discrete Appl. Math.. 2006;154:1947-1959.
Chapman S., García-Sánchez PA, Llena D., Ponomarenko V., Rosales J.. The catenary and tame degree in finitely generated commutative cancellative monoids. Manuscripta Math.. 2006;120:253-264.
Bras-Amorós M, García-Sánchez PA. Patterns on numerical semigroups. Linear Algebra Appl.. 2006;414:652-669.
2005
Rosales J., García-Sánchez PA. Pseudo-symmetric numerical semigroups with three generators. J. Algebra. 2005;291:46-54.
Rosales J., García-Sánchez PA, García-García JI, Branco MB. Numerical semigroups with a monotonic Apéry set. Czechoslovak Math. J.. 2005;55(130):755-772.
Rosales J., García-Sánchez PA, Urbano-Blanco J.. Correction to: ``Modular Diophantine inequalities and numerical semigroups'' [Pacific J. Math. \bf 218 (2005), no. 2, 379–398; \refcno 2218353]. Pacific J. Math.. 2005;220:199.
Rosales J., García-Sánchez PA, Urbano-Blanco J.. Modular Diophantine inequalities and numerical semigroups. Pacific J. Math.. 2005;218:379-398.
2004
Rosales J., García-Sánchez PA. Numerical semigroups with embedding dimension three. Arch. Math. (Basel). 2004;83:488-496.
García-Sánchez PA, Rosales JC. Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators. Ark. Mat.. 2004;42:301-306.
Rosales J., García-Sánchez PA, García-García JI, Madrid J.. Fundamental gaps in numerical semigroups with respect to their multiplicity. Acta Math. Sin. (Engl. Ser.). 2004;20:629-646.
Rosales J., García-Sánchez PA, García-García JI, Branco MB. Saturated numerical semigroups. Houston J. Math.. 2004;30:321-330 (electronic).
Rosales J., García-Sánchez PA, García-García JI, Branco MB. Arf numerical semigroups. J. Algebra. 2004;276:3-12.
Rosales J., García-Sánchez PA, García-García JI, Madrid J.. Fundamental gaps in numerical semigroups. J. Pure Appl. Algebra. 2004;189:301-313.
Rosales J., García-Sánchez PA, García-García JI. Every positive integer is the Frobenius number of a numerical semigroup with three generators. Math. Scand.. 2004;94:5-12.
Rosales J., García-Sánchez PA, García-García JI. Atomic commutative monoids and their elasticity. Semigroup Forum. 2004;68:64-86.
2003
Rosales J., García-Sánchez PA, García-García JI, Urbano-Blanco J.. Proportionally modular Diophantine inequalities. J. Number Theory. 2003;103:281-294.
Rosales J., García-Sánchez PA, García-García JI, Madrid J.. The oversemigroups of a numerical semigroup. Semigroup Forum. 2003;67:145-158.
Rosales J., García-Sánchez PA, García-García JI. Ideals of finitely generated commutative monoids. Semigroup Forum. 2003;66:305-322.
Rosales J., García-Sánchez PA, García-García JI, Branco MB. Numerical semigroups with maximal embedding dimension. Int. J. Commut. Rings. 2003;2:47-53.
2002
Chapman S., García-García JI, García-Sánchez PA, Rosales J.. On the number of factorizations of an element in an atomic monoid. Adv. in Appl. Math.. 2002;29:438-453.
Rosales J., García-Sánchez PA, García-García JI. Presentations of finitely generated submonoids of finitely generated commutative monoids. Internat. J. Algebra Comput.. 2002;12:659-670.
Rosales J., García-Sánchez PA, García-García JI, Branco MB. Systems of inequalities and numerical semigroups. J. London Math. Soc. (2). 2002;65:611-623.
García-Sánchez PA, Rosales J.. On Buchsbaum simplicial affine semigroups. Pacific J. Math.. 2002;202:329-339.
2001
Rosales J., García-Sánchez PA, García-García JI. Irreducible ideals of finitely generated commutative monoids. J. Algebra. 2001;238:328-344.
Rosales J., García-Sánchez PA. Minimal presentations of full subsemigroups of $\bold N^2$. Rocky Mountain J. Math.. 2001;31:1417-1422.
Chapman S., García-García JI, García-Sánchez PA, Rosales J.. Computing the elasticity of a Krull monoid. Linear Algebra Appl.. 2001;336:191-200.
Rosales J., García-Sánchez PA, García-García JI. Commutative ideal extensions of abelian groups. Semigroup Forum. 2001;62:311-316.
2000
Rosales JC, García-Sánchez PA, García-García JI. How to check if a finitely generated commutative monoid is a principal ideal commutative monoid. In: Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews). ACM, New York; 2000. 2. p. 288-291p. (electronic).
Rosales J., García-Sánchez PA. On the structure of simplicial affine semigroups. Proc. Roy. Soc. Edinburgh Sect. A. 2000;130:1017-1028.
Rosales J., García-Sánchez PA. Reduced commutative monoids with two Archimedean components. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8). 2000;3:471-484.
Rosales J., García-Sánchez PA. On full affine semigroups. J. Pure Appl. Algebra. 2000;149:295-303.
1999
Rosales J., García-Sánchez PA. On normal affine semigroups. Linear Algebra Appl.. 1999;286:175-186.
Rosales J., García-Sánchez PA. Presentations for subsemigroups of finitely generated commutative semigroups. Israel J. Math.. 1999;113:269-283.
Rosales J., García-Sánchez PA, Urbano-Blanco J.. On presentations of commutative monoids. Internat. J. Algebra Comput.. 1999;9:539-553.
García-Sánchez PA, Rosales J.. Numerical semigroups generated by intervals. Pacific J. Math.. 1999;191:75-83.
Rosales J., García-Sánchez PA. Finitely generated commutative monoids Nova Science Publishers, Inc., Commack, NY 1999.
Rosales J., García-Sánchez PA. On free affine semigroups. Semigroup Forum. 1999;58:367-385.
Rosales J., García-Sánchez PA. On the structure of Cohen-Macaulay simplicial affine semigroups. Comm. Algebra. 1999;27:511-518.
1998
Rosales J., García-Sánchez PA. On Cohen-Macaulay and Gorenstein simplicial affine semigroups. Proc. Edinburgh Math. Soc. (2). 1998;41:517-537.
Rosales J., García-Sánchez PA, Urbano-Blanco J.. On Cohen-Macaulay subsemigroups of $\bold N^2$. Comm. Algebra. 1998;26:2543-2558.
Rosales J., García-Sánchez PA. On numerical semigroups with high embedding dimension. J. Algebra. 1998;203:567-578.
Rosales J., García-Sánchez PA. Nonnegative elements of subgroups of $\bf Z^n$. Linear Algebra Appl.. 1998;270:351-357.
1995
Rosales J., García-Sánchez PA. On complete intersection affine semigroups. Comm. Algebra. 1995;23:5395-5412.