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A. Vigneron-Tenorio

Publications and source records attributed to A. Vigneron-Tenorio.

26 records · Page 2Linked to original sources
arXiv2016

Proportionally modular affine semigroups

This work introduces a new kind of semigroup of $\N^p$ called proportionally modular affine semigroup. These semigroups are defined by modular Diophantine inequalities and they are a generalization of proportionally modular numerical semigroups. We prove they are finitely generated and we give an algorithm to compute their minimal generating sets. We also specialise on the case $p=2$. For this case, we provide a faster algorithm to compute their minimal system of generators and we prove they are Cohen-Macaulay and Buchsbaum. Besides, the Gorenstein property is charactized, and their (minimal) Fröbenius vectors are determinated.

math.AC↗
arXiv2014

Affine convex body semigroups and Buchsbaum rings

In this work, new families of Buchsbaum rings, developed by mean of convex body semigroups, are presented. We characterize Buchsbaum circle and convex polygonal semigroups and describe algorithmic methods to check these characterizations.

math.AC↗
arXiv2014

Computation of Delta sets of numerical monoids

Let $\{a_1,\dots,a_p\}$ be the minimal generating set of a numerical monoid $S$. For any $s\in S$, its Delta set is defined by $Δ(s)=\{l_{i}-l_{i-1}|i=2,\dots,k\}$ where $\{l_1<\dots<l_k\}$ is the set $\{\sum_{i=1}^px_i\,|\, s=\sum_{i=1}^px_ia_i \textrm{ and } x_i\in \N \textrm{ for all }i\}.$ The Delta set of $S$, denoted by $Δ(S)$, is the union of all the sets $Δ(s)$ with $s\in S.$ As proved in [S.T. Chapman, R. Hoyer, and N. Kaplan. Delta sets of numerical monoids are eventually periodic. Aequationes Math. 77 (2009), no. 3, 273--279], there exists a bound $N$ such that $Δ(S)$ is the union of the sets $Δ(s)$ with $s\in S$ and $s<N$. In this work, by using geometrical tools, we obtain a sharpened bound and we give an algorithm to compute $Δ(S)$ from the factorizations of only $a_1$ elements.

math.AC↗
arXiv2013

Computing families of Cohen-Macaulay and Gorenstein rings

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-Macaulay/Gorenstein are given. We also provide some families of Cohen-Macaulay and Gorenstein rings.

math.AC↗
arXiv2012

Affine convex body semigroups

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 proportionally modular numerical semigroup of [7]. Several properties of these semigroups are proven. Affine convex body semigroups obtained from circles and polygons of R^2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them.

math.AC↗
arXiv2009

Simplicial complexes and minimal free resolution of monomial algebras

This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those algebras is related to the combinatorics of some simplicial complexes. Our description may be interpreted as an algorithmic procedure to partially compute this resolution.

math.AC↗