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arXiv · 1102.0096

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

Satoshi Murai·Eran Nevo
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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 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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Satoshi Murai, Eran Nevo. 2011-02-01. On the cd-index and gamma-vector of S*-shellable CW-spheres. https://arxiv.org/abs/1102.0096

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