A. Vigneron-Tenorio

activity

20102026

most citedAffine convex body semigroups

9 citations · 29 across the 28 of their papers we have counts for

collaborators

29 papers

math.AC2026

A note on strong affine semigroups

I. García-Marco, R. Tapia-Ramos, A. Vigneron-Tenorio

This work introduces and studies strong affine semigroups, extending the notion of strong numerical semigroups to the higher-dimensional setting. We show that non-numerical strong…

math.AC2025

On some affine semigroups characterized by a finite-state automata

J. I. Farrán, J. C. Rosales, R. Tapia-Ramos +1

This work introduces a new kind of affine semigroups called $P$ -semigroups. Within the framework of $C$ -semigroups, we define a finite-state automaton associated to them.…

math.AC2025

Affine semigroups without consecutive small elements

J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio

An $A$ -semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathc…

math.AC2024

A computational approach to the study of finite-complement submonids of an affine cone

J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio

Let $C \subseteq N^{p}$ be an integer cone. A $C$ -semigroup $S \subseteq C$ is an affine semigroup such that the set $C ∖ S$ is…

math.AC2024★ 1 cited

On ideals of affine semigroups and affine semigroups with maximal embedding dimension

J. I. García-García, R. Tapia-Ramos, A. Vigneron-Tenorio

Let $S \subseteq N^{p}$ be a semigroup, any $P \subseteq S$ is an ideal of $S$ if $P + S \subseteq P$ , and an $I (S)$ -semigroup is the affine semigroup $P \cup {0}$ , with $P$ an i…

math.AC2024

On the quotient of affine semigroups by a positive integer

J. I. García-García, R. Tapia-Ramos, A. Vigneron-Tenorio

This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tre…

math.RA2023

Some properties of affine $C$ -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…

math.AG2022

Conductors of Abhyankar-Moh semigroups of even degrees

Evelia R. GarcÍa Barroso, Juan Ignacio GarcÍa-GarcÍa, Luis José Santana SÁnchez +1

In their paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality, now known as the Abhyankar-Moh inequality, which can be stated in terms…

math.NT2022

The complexity of a numerical semigroup

J. I. García-García, M. A. Moreno-Frías, J. C. Rosales +1

Let $S$ and $Δ$ be numerical semigroups. A numerical semigroup $S$ is an $I (Δ)$ -{\it semigroup} if $S \ {0}$ is an ideal of $Δ$ . We will denote by $\mathcal{J}(Δ…

math.NT2021

On the ideal of some sumset semigroups

J. I. García-García, D. Marín-Aragón, A. Vigneron-Tenorio

A sumset semigroup is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. In this work, an algorithm for computing the ideals associ…

math.CO2020★ 2 cited

The Buchweitz set of a numerical semigroup

S. Eliahou, J. I. García-García, D. Marín-Aragón +1

Let $A \subset Z$ be a finite subset. We denote by $B (A)$ the set of all integers $n \geq 2$ such that $∣ n A ∣ > (2 n - 1) (∣ A ∣ - 1)$ , where $n A = A + \dots + A$ denotes the…

math.AG2020★ 1 cited

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.…

math.AC2020★ 1 cited

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…

math.AC2019

Characterizing affine $C$ -semigroups

J. D. Díaz-Ramírez, J. I. García-García, D. Marín-Aragón +1

Let $C \subset N^{p}$ be a finitely generated integer cone and $S \subset C$ be an affine semigroup such that the real cones generated by $C$ and by…

math.AC2019★ 1 cited

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 $f_{1} x_{1} + \dots + f_{n} x_{n} mod b \leq g_{1} x_{1} + \dots + g_{n} x_{n}$ w…

math.AC2019

Union of sets of lengths of numerical semigroups

J. I. García-García, D. Marín-Aragón, A. Vigneron-Tenorio

Let $S = ⟨ a_{1}, \dots, a_{p} ⟩$ be a numerical semigroup, $s \in S$ and $z (s)$ its set of factorizations. The set of length is denoted by ${\mathcal L}(s)=\{{\tt L}(x_1,…

math.AC2019

On pseudo-Frobenius elements of submonoids of $N^{d}$

J. I. García-García, I. Ojeda, J. C. Rosales +1

In this paper we study those submonoids of $N^{d}$ which a non-trivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associate…

math.AC2017★ 1 cited

Frobenius number and minimum genus of numerical semigroups with fixed multiplicity and embedding dimension

J. I. García-García, D. Marín-Aragón, M. A. Moreno-Frías +2

Fixed two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embeddi…

math.AC2017

Semigroups with fixed multiplicity and embedding dimension

J. I. García-García, D. Marín-Aragón, M. A. Moreno-Frías +2

Given $m \in N,$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in ${m, m + 1, \dots, 2 m - 1} .$ In…

math.NT2016★ 1 cited

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…

math.AC2015

Proportionally modular affine semigroups

J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio

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…

math.AC2015

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…

math.AC2014★ 4 cited

Computation of Delta sets of numerical monoids

J. I. García-García, M. A. Moreno-Frías, A. Vigneron-Tenorio

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<\do…

math.AC2014

Affine convex body semigroups and Buchsbaum rings

J. I. García-García, A. Sánchez-R. -Navarro, A. Vigneron-Tenorio

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 desc…

A note on strong affine semigroups

On some affine semigroups characterized by a finite-state automata

Affine semigroups without consecutive small elements

A computational approach to the study of finite-complement submonids of an affine cone

On ideals of affine semigroups and affine semigroups with maximal embedding dimension

On the quotient of affine semigroups by a positive integer

Some properties of affine C-semigroups

Conductors of Abhyankar-Moh semigroups of even degrees

The complexity of a numerical semigroup

On the ideal of some sumset semigroups

The Buchweitz set of a numerical semigroup

On reducible non-Weierstrass semigroups

Generalized strongly increasing semigroups

Characterizing affine C-semigroups

A geometrical characterization of proportionally modular affine semigroups

Union of sets of lengths of numerical semigroups

On pseudo-Frobenius elements of submonoids of Nd

Frobenius number and minimum genus of numerical semigroups with fixed multiplicity and embedding dimension

Semigroups with fixed multiplicity and embedding dimension

An extension of Wilf's conjecture to affine semigroups

Proportionally modular affine semigroups

A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings

Computation of Delta sets of numerical monoids

Affine convex body semigroups and Buchsbaum rings

Some properties of affine $C$ -semigroups

Characterizing affine $C$ -semigroups

On pseudo-Frobenius elements of submonoids of $N^{d}$