1506.03238Jun 10, 2015This paper has been withdrawn by the author due to a crucial error in Lemma $1.5$.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"
Depth and Stanley depth of the facet ideal associated to a line-type simplicial complex
Mircea Cimpoeas
Abstract
We consider the face ideal associated to a line-type simplicial complex. We compute the depth and the sdepth for its quotient ring. In particular, the facet ideal and its quotient ring satisfy the Stanley inequality.