Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Monday 4
Karen Yeats
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
Almost simplicial polytopes: the lower and upper bound theorems
Eran Nevo  1  , Guillermo Pineda-Villavicencio  2  , Julien Ugon  2  , David Yost  2  
1 : Institute of Mathematics, the Hebrew University of Jerusalem
2 : Centre for Informatics and Applied Optimisation, Federation University

This is an extended abstract of the full version. 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 bounds for the face numbers of 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

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