Depth and Stanley depth of the facet ideal associated to a line-type simplicial complex

TL;DR

This paper investigates the algebraic properties of the face ideal of a line-type simplicial complex, specifically computing depth and Stanley depth, and confirms they satisfy the Stanley inequality.

Contribution

It provides explicit calculations of depth and Stanley depth for the facet ideal of line-type simplicial complexes, confirming the Stanley inequality holds.

Findings

Depth and Stanley depth are computed explicitly.

The facet ideal and its quotient satisfy the Stanley inequality.

Results contribute to understanding algebraic invariants of simplicial complexes.

Abstract

We consider the face ideal associated to a line-type simplicial complex. We compute the \texttt{depth} and the \texttt{sdepth} for its quotient ring. In particular, the facet ideal and its quotient ring satisfy the Stanley inequality.