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 1
Externally publishedYes

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Simplicial Complex
F-vector
Polynomial
Polytopes
Polytope

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the cd-index and γ-vector of S*-shellable CW-spheres. / Murai, Satoshi; Nevo, Eran.

In: Mathematische Zeitschrift, Vol. 271, No. 3-4, 01.08.2012, p. 1309-1319.

Research output: Contribution to journalArticle

Murai, Satoshi ; Nevo, Eran. / On the cd-index and γ-vector of S*-shellable CW-spheres. In: Mathematische Zeitschrift. 2012 ; Vol. 271, No. 3-4. pp. 1309-1319.
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