Almost simplicial polytopes: the lower and upper bound theorems

Nevo, Eran, Pineda-Villavicencio, Guillermo, Ugon, Julien and Yost, David 2019, Almost simplicial polytopes: the lower and upper bound theorems, Canadian journal of mathematics, 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 orcid.org/0000-0001-5290-8051
Yost, David
Journal name Canadian journal of mathematics
Total pages 20
Publisher Cambridge Univeristy Press
Place of publication Cambridge, Eng.
Publication date 2019
ISSN 0008-414X
1496-4279
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.
Notes In Press
Language eng
DOI 10.4153/s0008414x18000123
Field of Research 0101 Pure Mathematics
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2018, Canadian Mathematical Society
Persistent URL http://hdl.handle.net/10536/DRO/DU:30123275

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