An inequality between depth and Stanley depth

TL;DR

This paper proves that for square free monomial ideals in five variables, the Stanley depth is always at least as large as the depth, confirming Stanley's Conjecture in this specific case.

Contribution

It establishes the validity of Stanley's Conjecture for square free monomial ideals in five variables, a previously unresolved case.

Findings

Stanley's Conjecture holds for square free monomial ideals in five variables.

The Stanley depth is greater than or equal to the depth for these ideals.

Provides a proof confirming the conjecture in this specific setting.

Abstract

We show that Stanley's Conjecture holds for square free monomial ideals in five variables, that is the Stanley depth of a square free monomial ideal in five variables is greater or equal with its depth.