On the cd-index and γ-vector of S*-shellable CW-spheres

Satoshi Murai, Eran Nevo

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We show that the γ-vector of the order complex of any polytope is the f-vector of a balanced simplicial complex. This is done by proving this statement for a subclass of Stanley's S-shellable CW-spheres which includes all polytopes. The proof shows that certain parts of the cd-index, when specializing c = 1 and considering the resulted polynomial in d, are the f-polynomials of simplicial complexes that can be colored with "few" colors. We conjecture that the cd-index of a regular CW-sphere is itself the flag f-vector of a colored simplicial complex in a certain sense.

Original languageEnglish
Pages (from-to)1309-1319
Number of pages11
JournalMathematische Zeitschrift
Volume271
Issue number3-4
DOIs
Publication statusPublished - 2012 Aug

Keywords

  • Balanced simplicial complex
  • Polytope
  • cd-index
  • γ-vector

ASJC Scopus subject areas

  • Mathematics(all)

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