On the behavior of the size of a monomial ideal

TL;DR

This paper investigates how the size of monomial ideals changes under polarization and deformations, extending known results relating size and Stanley depth for squarefree monomial ideals.

Contribution

It introduces new insights into the behavior of monomial ideal size under polarization and deformations, extending prior results on Stanley depth.

Findings

Size behavior under polarization and deformations analyzed

Extended relation between size and Stanley depth for squarefree monomial ideals

Generalized previous results by Herzog, Popescu, Vladoiu, and Tang

Abstract

In this paper we study the behavior of the size of a monomial ideal under polarization and under generic deformations. As an application, we extend a result relating the size and the Stanley depth of a squarefree monomial ideal obtained by Herzog, Popescu and Vladoiu, together with a parallel result obtained by Tang.