A note on Stanley's conjecture for monomial ideals

TL;DR

This paper proves Stanley's conjecture for monomial ideals generated by at most 2n-1 monomials, establishing that the Stanley depth is at least the depth for these cases.

Contribution

It demonstrates that Stanley's conjecture holds for a new class of monomial ideals with a bounded number of generators.

Findings

Stanley's conjecture verified for monomial ideals with ≤ 2n-1 generators

sdepth(I) ≥ depth(I) for these ideals

Expands the class of ideals satisfying Stanley's conjecture

Abstract

We prove that the Stanley's conjecture holds for monomial ideals $I\subset K[x_1,...,x_n]$ generated by at most $2n-1$ monomials, i.e. $sdepth(I)\geq depth(I)$.