Stanley depth of complete intersection monomial ideals and upper-discrete partitions

TL;DR

This paper determines the Stanley depth of complete intersection monomial ideals and explores upper-discrete structures, providing explicit formulas and results for specific classes of monomial ideals.

Contribution

It establishes a formula for the Stanley depth of complete intersection monomial ideals and analyzes upper-discrete structures, especially for squarefree ideals generated by three elements.

Findings

Stanley depth of $I$ is $n - loor{m/2}$ for complete intersection monomial ideals.

If $I$ is a squarefree monomial ideal generated by 3 elements, its Stanley depth is $n - 1$.

Provides insights into the structure of monomial ideals through upper-discrete partitions.

Abstract

Let $I$ be an $m$-generated complete intersection monomial ideal in $S=K[x_1,...,x_n]$. We show that the Stanley depth of $I$ is $n-\floor{\frac{m}{2}}$. We also study the upper-discrete structure for monomial ideals and prove that if $I$ is a squarefree monomial ideal minimally generated by 3 elements, then the Stanley depth of $I$ is $n-1$.