9 citations · 27 across the 16 of their papers we have counts for
17 papers
Some properties of affine -semigroups
Juan Ignacio García-García, Daniel Marín-Aragón, Adrián Sánchez-Loureiro +1
Numerical semigroups have been extensively studied throughout the literature, and many of their invariants have been characterized. In this work, we generalize some of the most imp…
The complexity of a numerical semigroup
J. I. García-García, M. A. Moreno-Frías, J. C. Rosales +1
Let and be numerical semigroups. A numerical semigroup is an -{\it semigroup} if is an ideal of . We will denote by $\mathcal{J}(Δ…
The Buchweitz set of a numerical semigroup
S. Eliahou, J. I. García-García, D. Marín-Aragón +1
Let be a finite subset. We denote by the set of all integers such that , where denotes the…
On reducible non-Weierstrass semigroups
J. I. García-García, D. Marín-Aragón, F. Torres +1
Weierstrass semigroups are well-known along the literature. We present a new family of non-Weierstrass semigroups which can be written as an intersection of Weierstrass semigroups.…
Generalized strongly increasing semigroups
E. R. García Barroso, J. I. García-García, A. Vigneron-Tenorio
In this work we present a new class of numerical semigroups called GSI-semigroups. We see the relations between them and others families of semigroups and we give explicitly their…
A geometrical characterization of proportionally modular affine semigroups
J. D. Díaz-Ramírez, J. I. García-García, A. Sánchez-R. -Navarro +1
A proportionally modular affine semigroup is the set of nonnegative integer solutions of a modular Diophantine inequality w…
Union of sets of lengths of numerical semigroups
J. I. García-García, D. Marín-Aragón, A. Vigneron-Tenorio
Let be a numerical semigroup, and its set of factorizations. The set of length is denoted by ${\mathcal L}(s)=\{{\tt L}(x_1,…
An extension of Wilf's conjecture to affine semigroups
J. I. García-García, D. Marín-Aragón, A. Vigneron-Tenorio
Let $\CaC\subset \Q^p$ be a rational cone. An affine semigroup $S\subset \CaC$ is a $\CaC$-semigroup whenever $(\CaC\setminus S)\cap \N^p$ has only a finite number of elements. In…
Proportionally modular affine semigroups
J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio
This work introduces a new kind of semigroup of called proportionally modular affine semigroup. These semigroups are defined by modular Diophantine inequalities and they are…
On divisor-closed submonoids and minimal distances in finitely generated monoids
J. I. García-García, D. Marín-Aragón, M. A. Moreno-Frías
We study the lattice of divisor-closed submonoids of finitely generated cancellative commutative monoids. In case the monoid is an affine semigroup, we give a geometrical character…
A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings
Juan Ignacio García-García, Daniel Marín-Aragón, Alberto Vigneron-Tenorio
We provide algorithmic methods to check the Cohen--Macaulayness, Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are constructed from the dilation of bo…
Computation of Delta sets of numerical monoids
J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio
Let be the minimal generating set of a numerical monoid . For any , its Delta set is defined by where $\{l_1<\do…
Computation of the w-primality and asymptotic w-primality with applications to numerical semigroups
J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio
We give an algorithm to compute the -primality of finitely generated atomic monoids. Asymptotic $\w$-primality is also studied and a formula to obtain it in finitely generated q…
Computing families of Cohen-Macaulay and Gorenstein rings
J. I. García-García, A. Vigneron-Tenorio
We characterize Cohen-Macaulay and Gorenstein rings obtained from certain types of convex body semigroups. Algorithmic methods to check if a polygonal or circle semigroup is Cohen-…
Affine convex body semigroups
J. I. García-García, M. A. Moreno-Frías, A. Sánchez-R. -Navarro +1
In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. They generalize to arbitrary dimension the concept of p…
Combinatorial properties and characterization of glued semigroups
J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are genera…
On the decomposable semigroups and applications
Juan Ignacio García-García, M. Ángeles Moreno-Frías, Alberto Vigneron-Tenorio
The aim of this work is to reduce the complexity of the available algorithms for computing the generator sets of a semigroup ideal by using the Hermite normal form. In order to ach…