Spheres arising from multicomplexes

Satoshi Murai*

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

In 1992, Thomas Bier introduced a surprisingly simple way to construct a large number of simplicial spheres. He proved that, for any simplicial complex δ on the vertex set V with δ≢2V, the deleted join of δ with its Alexander dual δ∨ 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.

本文言語English
ページ(範囲)2167-2184
ページ数18
ジャーナルJournal of Combinatorial Theory. Series A
118
8
DOI
出版ステータスPublished - 2011 11月
外部発表はい

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学
  • 計算理論と計算数学

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