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Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

Almost simplicial polytopes: the lower and upper bound theorems

Résumé

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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Dates et versions

hal-02166344 , version 1 (26-06-2019)

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Eran Nevo, Guillermo Pineda-Villavicencio, Julien Ugon, David Yost. Almost simplicial polytopes: the lower and upper bound theorems. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6369⟩. ⟨hal-02166344⟩
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