Eran Nevo ; Guillermo Pineda-Villavicencio ; Julien Ugon ; David Yost - Almost simplicial polytopes: the lower and upper bound theorems

dmtcs:6369 - Discrete Mathematics & Theoretical Computer Science, April 22, 2020, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) - https://doi.org/10.46298/dmtcs.6369
Almost simplicial polytopes: the lower and upper bound theoremsArticle

Authors: Eran Nevo 1; Guillermo Pineda-Villavicencio ORCID2; Julien Ugon ORCID2; David Yost ORCID2

  • 1 Einstein Institute of Mathematics
  • 2 Centre for Informatics and Applied Optimization

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.


Volume: DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
Published on: April 22, 2020
Imported on: July 4, 2016
Keywords: Combinatorics,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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