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

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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.

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Authors and Affiliations

  1. Department of Mathematical Science, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi, 753-8512, Japan

    Satoshi Murai

  2. Department of Mathematics, Ben Gurion University of the Negev, 84105, Be’er Sheva, Israel

    Eran Nevo

Authors
  1. Satoshi Murai
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  2. Eran Nevo
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Corresponding author

Correspondence to Eran Nevo.

Additional 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.

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Murai, S., Nevo, E. On the cd-index and γ-vector of S*-shellable CW-spheres. Math. Z. 271, 1309–1319 (2012). https://doi.org/10.1007/s00209-011-0917-4

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  • DOI: https://doi.org/10.1007/s00209-011-0917-4

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