On the Stanley depth of the path ideal of a cycle graph

TL;DR

This paper establishes precise bounds for the Stanley depth of the quotient ring of the path ideal in a cycle graph, confirming it satisfies the Stanley inequality, thus advancing understanding in combinatorial commutative algebra.

Contribution

It provides tight bounds for the Stanley depth of cycle graph path ideals and proves the Stanley inequality holds for these cases.

Findings

Stanley depth bounds are tight for cycle graph path ideals

The Stanley inequality is satisfied for these ideals

Advances understanding of algebraic properties of graph-based ideals

Abstract

We give tight bounds for the Stanley depth of the quotient ring of the path ideal of a cycle graph. In particular, we prove that it satisfies the Stanley inequality.