Special Stanley Decompositions

TL;DR

This paper presents a special Stanley decomposition for intersections of three monomial prime ideals, establishing a lower bound for Stanley depth that confirms Stanley's Conjecture in this case.

Contribution

It introduces a specific Stanley decomposition for such intersections, proving the conjecture holds for these ideals.

Findings

Stanley's Conjecture holds for intersections of three monomial prime ideals.

Provides a lower bound for Stanley depth equal to the depth of the ideal.

Offers a constructive decomposition method for these ideals.

Abstract

Let $I$ be an intersection of three monomial prime ideals of a polynomial algebra $S$ over a field. We give a special Stanley decomposition of $I$ which provides a lower bound of the Stanley depth of $I$, greater than or equal to $\depth\ (I)$, that is, Stanley's Conjecture holds for $I$.