Almost simplicial polytopes

Sun, 29/11/2015 - 14:00
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Abstract: 
We study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called 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 $s=0$. We characterize the minimizers and provide examples of maximizers, for any $d$.

Time permitting, I'll also discuss results on reconstruction problems for these and for related polytopes.

This is joint work with Guillermo Pineda-Villavicencio, Julien Ugon, David Yost.