Spheres arising from multicomplexes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Murai, Satoshi

关键词: Bier spheres;    Alexander duality;    Shellability;    Edge decomposability;    Polarization;   

DOI  :  10.1016/j.jcta.2011.04.015

来源: Elsevier

【 摘 要 】

In 1992, Thomas Bier introduced a surprisingly simple way to construct a large number of simplicial spheres. He proved that, for any simplicial complex Delta on the vertex set V with Delta not equal 2(v) the deleted join of Delta with its Alexander dual Delta(v) is a combinatorial sphere. In this paper, we extend Bier's construction to multicomplexes, and study their combinatorial and algebraic properties. We show that all these spheres are shellable and edge decomposable. which yields a new class of many shellable edge decomposable spheres that are not realizable as polytopes. It is also shown that these spheres are related to polarizations and Alexander duality for monomial ideals which appear in commutative algebra theory. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free