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arXiv · 1411.3567

The face ideal of a simplicial complex

Jürgen Herzog·Takayuki Hibi
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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.

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Jürgen Herzog, Takayuki Hibi. 2014-11-13. The face ideal of a simplicial complex. https://arxiv.org/abs/1411.3567

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