Publications

2018
Delta sets for nonsymmetric numerical semigroups with embedding dimension three. Forum Math.. 2018;30:15-30.
2017
Parametrizing Arf numerical semigroups. J. Algebra Appl.. 2017;16:1750209, 31.
Delta sets for symmetric numerical semigroups with embedding dimension three. Aequationes Math.. 2017;91:579-600.
Bases of subalgebras of $\BbbK[\![x]\!]$ and $\BbbK[x]$. J. Symbolic Comput.. 2017;79:4-22.
2016
Numerical semigroups and applications. Vol 1 Springer, [Cham] 2016.
$\ssfnumericalsgps$, a $\ssfGAP$ package for numerical semigroups. ACM Commun. Comput. Algebra. 2016;50:12-24.
Cyclotomic numerical semigroups. SIAM J. Discrete Math.. 2016;30:650-668.
Algorithms for curves with one place at infinity. J. Symbolic Comput.. 2016;74:475-492.
Measuring primality in numerical semigroups with embedding dimension three. J. Algebra Appl.. 2016;15:1650007, 16.
Numerical semigroups with a given set of pseudo-Frobenius numbers. LMS Journal of Computation and Mathematics. 2016;19(1):186-205.
2015
When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three. Involve. 2015;8:677-694.
Frobenius vectors, Hilbert series and gluings of affine semigroups. J. Commut. Algebra. 2015;7:317-335.
numericalsgps, an accepted GAP package 2015.
The second Feng-Rao number for codes coming from inductive semigroups. IEEE Trans. Inform. Theory. 2015;61:4938-4947.
On the number of $\ssfL$-shapes in embedding dimension four numerical semigroups. Discrete Math.. 2015;338:2168-2178.
2014
On the weight hierarchy of codes coming from semigroups with two generators. IEEE Trans. Inform. Theory. 2014;60:282-295.
Constructing almost symmetric numerical semigroups from irreducible numerical semigroups. Comm. Algebra. 2014;42:1362-1367.
Homogenization of a nonsymmetric embedding-dimension-three numerical semigroup. Involve. 2014;7:77-96.
2013
Nonhomogeneous patterns on numerical semigroups. Internat. J. Algebra Comput.. 2013;23:1469-1483.
Huneke-Wiegand Conjecture for complete intersection numerical semigroup rings. J. Algebra. 2013;391:114-124.
Constructing the set of complete intersection numerical semigroups with a given Frobenius number. Appl. Algebra Engrg. Comm. Comput.. 2013;24:133-148.
Numerical semigroups problem list 2013.
On the generalized Feng-Rao numbers of numerical semigroups generated by intervals. Math. Comp.. 2013;82:1813-1836.
2012
On the delta set and the Betti elements of a BF-monoid. Arab. J. Math. (Springer). 2012;1:53-61.
Minimal presentations for monoids with the ascending chain condition on principal ideals. Semigroup Forum. 2012;85:185-190.
2011
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. Illinois J. Math.. 2011;55:1385-1414 (2013).
Counting numerical semigroups with short generating functions. Internat. J. Algebra Comput.. 2011;21:1217-1235.
Elements in a numerical semigroup with factorizations of the same length. Canad. Math. Bull.. 2011;54:39-43.
2010
Uniquely presented finitely generated commutative monoids. Pacific J. Math.. 2010;248:91-105.
Factoring in embedding dimension three numerical semigroups. Electron. J. Combin.. 2010;17:Research Paper 138, 21.
2009
Numerical semigroups. Vol 20 Springer, New York 2009.
The catenary and tame degree of numerical monoids. Forum Math.. 2009;21:117-129.
2008
Strongly taut finitely generated monoids. Monatsh. Math.. 2008;155:119-124.
Every numerical semigroup is one half of infinitely many symmetric numerical semigroups. Comm. Algebra. 2008;36:2910-2916.
The set of solutions of a proportionally modular Diophantine inequality. J. Number Theory. 2008;128:453-467.
Numerical semigroups having a Toms decomposition. Canad. Math. Bull.. 2008;51:134-139.
Every numerical semigroup is one half of a symmetric numerical semigroup. Proc. Amer. Math. Soc.. 2008;136:475-477 (electronic).
Systems of proportionally modular Diophantine inequalities. Semigroup Forum. 2008;76:469-488.
2006
Numerical semigroups mini-course 2006.
Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations. Discrete Appl. Math.. 2006;154:1947-1959.
The catenary and tame degree in finitely generated commutative cancellative monoids. Manuscripta Math.. 2006;120:253-264.
Patterns on numerical semigroups. Linear Algebra Appl.. 2006;414:652-669.
2005
Modular Diophantine inequalities and numerical semigroups. Pacific J. Math.. 2005;218:379-398.
Pseudo-symmetric numerical semigroups with three generators. J. Algebra. 2005;291:46-54.
Numerical semigroups with a monotonic Apéry set. Czechoslovak Math. J.. 2005;55(130):755-772.
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.
2004
Atomic commutative monoids and their elasticity. Semigroup Forum. 2004;68:64-86.
Numerical semigroups with embedding dimension three. Arch. Math. (Basel). 2004;83:488-496.
Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators. Ark. Mat.. 2004;42:301-306.
Fundamental gaps in numerical semigroups with respect to their multiplicity. Acta Math. Sin. (Engl. Ser.). 2004;20:629-646.
Saturated numerical semigroups. Houston J. Math.. 2004;30:321-330 (electronic).
Arf numerical semigroups. J. Algebra. 2004;276:3-12.
Fundamental gaps in numerical semigroups. J. Pure Appl. Algebra. 2004;189:301-313.
Every positive integer is the Frobenius number of a numerical semigroup with three generators. Math. Scand.. 2004;94:5-12.
2003
Numerical semigroups with maximal embedding dimension. Int. J. Commut. Rings. 2003;2:47-53.
Proportionally modular Diophantine inequalities. J. Number Theory. 2003;103:281-294.
The oversemigroups of a numerical semigroup. Semigroup Forum. 2003;67:145-158.
Ideals of finitely generated commutative monoids. Semigroup Forum. 2003;66:305-322.
2002
On the number of factorizations of an element in an atomic monoid. Adv. in Appl. Math.. 2002;29:438-453.
Presentations of finitely generated submonoids of finitely generated commutative monoids. Internat. J. Algebra Comput.. 2002;12:659-670.
Systems of inequalities and numerical semigroups. J. London Math. Soc. (2). 2002;65:611-623.
On Buchsbaum simplicial affine semigroups. Pacific J. Math.. 2002;202:329-339.
2001
Commutative ideal extensions of abelian groups. Semigroup Forum. 2001;62:311-316.
Irreducible ideals of finitely generated commutative monoids. J. Algebra. 2001;238:328-344.
Minimal presentations of full subsemigroups of $\bold N^2$. Rocky Mountain J. Math.. 2001;31:1417-1422.
Computing the elasticity of a Krull monoid. Linear Algebra Appl.. 2001;336:191-200.
2000
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).
On the structure of simplicial affine semigroups. Proc. Roy. Soc. Edinburgh Sect. A. 2000;130:1017-1028.
Reduced commutative monoids with two Archimedean components. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8). 2000;3:471-484.
On full affine semigroups. J. Pure Appl. Algebra. 2000;149:295-303.
1999
On the structure of Cohen-Macaulay simplicial affine semigroups. Comm. Algebra. 1999;27:511-518.
On normal affine semigroups. Linear Algebra Appl.. 1999;286:175-186.
Presentations for subsemigroups of finitely generated commutative semigroups. Israel J. Math.. 1999;113:269-283.
On presentations of commutative monoids. Internat. J. Algebra Comput.. 1999;9:539-553.
Numerical semigroups generated by intervals. Pacific J. Math.. 1999;191:75-83.
Finitely generated commutative monoids Nova Science Publishers, Inc., Commack, NY 1999.
On free affine semigroups. Semigroup Forum. 1999;58:367-385.
1998
On Cohen-Macaulay and Gorenstein simplicial affine semigroups. Proc. Edinburgh Math. Soc. (2). 1998;41:517-537.
On Cohen-Macaulay subsemigroups of $\bold N^2$. Comm. Algebra. 1998;26:2543-2558.
On numerical semigroups with high embedding dimension. J. Algebra. 1998;203:567-578.
Nonnegative elements of subgroups of $\bf Z^n$. Linear Algebra Appl.. 1998;270:351-357.
1995
On complete intersection affine semigroups. Comm. Algebra. 1995;23:5395-5412.