Philippe Gimenez

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math.AC2026

Generalized AndrÃ¡sfai graphs and special Betti diagrams of edge ideals

Sara Asensio, Ignacio GarcÃa-Marco, Philippe Gimenez

Edge ideals of graphs were introduced by Villarreal in 1990, and have been the subject of many studies since then. In the same year, FrÃ¶berg characterized edge ideals with regular…

math.AC2025

Sifted degrees of the equations of the Rees module and their connection with the Artin-Rees numbers

Philippe Gimenez, Francesc Planas-Vilanova

Let $A$ be a noetherian ring, $I$ an ideal of $A$ and $N \subset M$ finitely generated $A$ -modules. The relation type of $I$ with respect to $M$ , denoted by $rt (I; M)$ , is th…

math.AC2025

Computational Aspects of the Short Resolution

Ignacio GarcÃa-Marco, Philippe Gimenez, Mario GonzÃ¡lez-SÃ¡nchez

Let $R := k [x_{1}, \dots, x_{n}]$ be a polynomial ring over a field $k$ , $I \subset R$ be a homogeneous ideal with respect to a weight vector $Ï= (Ï_1,\ldots,Ï_n) \in (\math…

math.AC2025

Proyective Cohen-Macaulay monomial curves and their affine charts

Ignacio GarcÃa-Marco, Philippe Gimenez, Mario GonzÃ¡lez-SÃ¡nchez

In this paper, we explore when the Betti numbers of the coordinate rings of a projective monomial curve and one of its affine charts are identical. Given an infinite field $k$ and…