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arXiv · 1510.08258

Almost simplicial polytopes I. The lower and upper bound theorems

Eran Nevo·Guillermo Pineda-Villavicencio·Julien Ugon·David Yost
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Abstract

We study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called {\it almost simplicial polytopes}. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$ and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case of $s=0$. We characterize the minimizers and provide examples of maximizers, for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.

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Eran Nevo, Guillermo Pineda-Villavicencio, Julien Ugon, David Yost. 2015-10-28. Almost simplicial polytopes I. The lower and upper bound theorems. https://arxiv.org/abs/1510.08258

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