Stanley depth of weakly polymatroidal ideals

TL;DR

This paper proves that Stanley's conjecture is valid for the quotient of a polynomial ring by weakly polymatroidal ideals, expanding the class of ideals for which the conjecture holds.

Contribution

It demonstrates that Stanley's conjecture holds for weakly polymatroidal ideals, a significant extension in the understanding of Stanley depth.

Findings

Stanley's conjecture verified for weakly polymatroidal ideals

Extension of classes of ideals satisfying Stanley's conjecture

Provides new insights into the structure of weakly polymatroidal ideals

Abstract

Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,\dots,x_n]$ be the polynomial ring in $n$ variables over the field $\mathbb{K}$. In this paper, it is shown that Stanley's conjecture holds for $S/I$, if $I$ is a weakly polymatroidal ideal.