Stanley depth of monomial ideals

TL;DR

This paper investigates the Stanley depth of monomial ideals and explores conditions under which the Stanley Conjecture holds for the quotient of two such ideals, utilizing recent polarization results.

Contribution

It provides new insights into the Stanley Conjecture for monomial ideals by applying recent polarization techniques to analyze when the conjecture is valid.

Findings

Identifies conditions for the Stanley Conjecture to hold for I/J

Utilizes recent polarization results to analyze monomial ideals

Advances understanding of Stanley depth in polynomial algebras

Abstract

Let $I\supsetneq J$ be two monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . We study when the Stanley Conjecture holds for $I/J$ using the recent result of \cite{IKM} concerning the polarization.