S. Eliahou

activity

20052025

most citedMonomial ideals with tiny squares

22 citations · 122 across the 24 of their papers we have counts for

collaborators

27 papers

math.NT2025

A Normality Conjecture on Rational Base Number Systems

Mélodie Andrieu, Shalom Eliahou, Léo Vivion

The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two…

math.NT2025

The number system in rational base $3/2$ and the $3 x + 1$ problem

Shalom Eliahou, Jean-Louis Verger-Gaugry

The representation of numbers in rational base $p / q$ was introduced in 2008 by Akiyama, Frougny & Sakarovitch, with a special focus on the case $p / q = 3/2$ . Unnoticed since then, nat…

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…

math.NT2021★ 1 cited

Is the Syracuse falling time bounded by 12?

Shalom Eliahou, Jean Fromentin, Rénald Simonetto

Let $T : N \to N$ denote the $3 x + 1$ function, where $T (n) = n /2$ if $n$ is even, $T (n) = (3 n + 1) /2$ if $n$ is odd. As an accelerated version of $T$ , we define a j…