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arXiv · 1209.1789

gamma-vectors of edge subdivisions of the boundary of the cross polytope

Natalie Aisbett
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Abstract

For any flag simplicial complex $Θ$ obtained by stellar subdividing the boundary of the cross polytope in edges, we define a flag simplicial complex $Γ(Θ)$ (dependent on the sequence of subdivisions) whose $f$-vector is the $γ$-vector of $Θ$. This proves that the $γ$-vector of any such simplicial complex satisfies the Frankl-Füredi-Kalai inequalities, partially solving a conjecture by Nevo and Petersen \cite{np}. We show that when $Θ$ is the dual simplicial complex to a nestohedron, and the sequence of subdivisions corresponds to a flag ordering as defined in \cite{ai}, that $Γ(Θ)$ is equal to the flag simplical complex defined there.

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Natalie Aisbett. 2012-09-09. gamma-vectors of edge subdivisions of the boundary of the cross polytope. https://arxiv.org/abs/1209.1789

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