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

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.

This paper has been withdrawn by the author due to a crucial error in Lemma $1.5$. Also, the main result of the paper was restated in the paper "Stanley depth of the path ideal associated to a line graph"

References in corpus (2)

• A non-partitionable Cohen-Macaulay simplicial complex
• Stanley depth of powers of the path ideal