On the Stanley depth of edge ideals of k-partite clutters

TL;DR

This paper establishes upper bounds for the Stanley depth of edge ideals in k-partite clutters, generalizes previous results for bipartite graphs, and confirms Stanley's conjecture for certain uniform complete k-partite clutters.

Contribution

It provides new upper bounds for Stanley depth, generalizes known results to k-partite clutters, and offers a shorter proof for Stanley's conjecture in specific cases.

Findings

Upper bounds for Stanley depth of edge ideals of k-partite clutters.

Generalization of results from bipartite to k-partite cases.

Validation of Stanley's conjecture for d-uniform complete d-partite clutters.

Abstract

We give upper bounds for the Stanley depth of edge ideals of certain k-partite clutters. In particular, we generalize a result of Ishaq about the Stanley depth of the edge ideal of a complete bipartite graph. A result of Pournaki, Seyed Fakhari and Yassemi implies that the Stanley's conjecture holds for d-uniform complete d-partite clutters. Here we give a shorter and different proof of this fact.