S. Eliahou

activity

20052025

most citedMonomial ideals with tiny squares

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

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5 papers · 1 filter

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.AC2020

Iterated sumsets and Hilbert functions

Shalom Eliahou, Eshita Mazumdar

Let A be a finite subset of an abelian group (G, +). Let h $\geq$ 2 be an integer. If |A| $\geq$ 2 and the cardinality |hA| of the h-fold iterated sumset hA = A + $\times$ $\times$ $…

math.AC2019★ 1 cited

Gotzmann Monomials In Four Variables

V Bonanzinga, Shalom Eliahou

It is a widely open problem to determine which monomials in the n-variable polynomial ring $K [x_{1}, ..., x_{n}]$ over a field $K$ have the Gotzmann property, i.e. induce a Borel-stable…

math.AC2018★ 22 cited

Monomial ideals with tiny squares

Shalom Eliahou, Jürgen Herzog, Maryam Mohammadi Saem

Let $I \subset K [x, y]$ be a monomial ideal. How small can $μ (I^{2})$ be in terms of $μ (I)$ ? It has been expected that the inequality $μ (I^{2}) > μ (I)$ should hold whenever $μ (I) \geq 2$ …