Almost simplicial polytopes: the lower and upper bound theorems

Nevo, Eran, Pineda-Villavicencio, Guillermo, Ugon, Julien and Yost, David 2020, Almost simplicial polytopes: the lower and upper bound theorems, Canadian journal of mathematics, vol. 72, no. 2, pp. 537-556, doi: 10.4153/s0008414x18000123.

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Title Almost simplicial polytopes: the lower and upper bound theorems
Author(s) Nevo, Eran
Pineda-Villavicencio, Guillermo
Ugon, JulienORCID iD for Ugon, Julien
Yost, David
Journal name Canadian journal of mathematics
Volume number 72
Issue number 2
Start page 537
End page 556
Total pages 20
Publisher Cambridge University Press
Place of publication Cambridge, Eng.
Publication date 2020-04
ISSN 0008-414X
Summary We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of , and , thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where . We characterize the minimizers and provide examples of maximizers for any . Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.
Language eng
DOI 10.4153/s0008414x18000123
Indigenous content off
Field of Research 0101 Pure Mathematics
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2018, Canadian Mathematical Society
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