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

Satoshi Murai, Eran Nevo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageAmerican English
Pages (from-to)1309-1319
Number of pages11
JournalMathematische Zeitschrift
Issue number3-4
StatePublished - Aug 2012
Externally publishedYes

Bibliographical note

Funding Information:
Research of the first author was partially supported by KAKENHI 22740018. Research of the second author was partially supported by an NSF Award DMS-0757828 and Marie Curie grant IRG-270923.


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


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