Serre's Condition, Balanced Simplicial Complexes, and Higher Nerves
Brent Holmes, Justin Lyle · arXiv (Cornell University) · 2018
We establish relationships between simplicial complexes satisfying Serre's condition $(S_{\ell})$ and the vanishing of reduced homologies of their higher nerve complexes. We further study the behavior of rank selected subcomplexes of balanced $(S_{\ell})$ complexes, and, generalizing results of Stanley and Hibi, we prove that these subcomplexes retain $(S_{\ell})$.