Shalom Eliahou

collaborators

3 papers

math.AC2024

On the Gotzmann threshold of monomials

Vittoria Bonanzinga, Shalom Eliahou

Let $R_{n} = K [x_{1}, \dots, x_{n}]$ be the $n$ -variable polynomial ring over a field $K$ . Let $S_{n}$ denote the set of monomials in $R_{n}$ . A monomial $u \in S_{n}$ is a \textit{Gotzmann monomi…

math.AC2023

Optimal Bounds on the Growth of Iterated Sumsets in Abelian Semigroups

Shalom Eliahou, Eshita Mazumdar

We provide optimal upper bounds on the growth of iterated sumsets $h A = A + \dots + A$ for finite subsets $A$ of abelian semigroups. More precisely, we show that the new upper bounds rec…

math.GR2023

A verification of Wilf's conjecture up to genus 100

Manuel Delgado, Shalom Eliahou, Jean Fromentin

For a numerical semigroup $S \subseteq N$ , let $m, e, c, g$ denote its multiplicity, embedding dimension, conductor and genus, respectively. Wilf's conjecture (1978) states t…