The face ideal of a simplicial complex
Commutative Algebra
2014-11-25 v2
Abstract
Given a simplicial complex we associate to it a squarefree monomial ideal which we call the face ideal of the simplicial complex, and show that it has linear quotients. It turns out that its Alexander dual is a whisker complex. We apply this construction in particular to chain and antichain ideals of a finite partially ordered set. We also introduce so-called higher dimensional whisker complexes and show that their independence complexes are shellable.
Cite
@article{arxiv.1411.3567,
title = {The face ideal of a simplicial complex},
author = {Jürgen Herzog and Takayuki Hibi},
journal= {arXiv preprint arXiv:1411.3567},
year = {2014}
}