On the cone of f-vectors of cubical polytopes

Ron M. Adin; Daniel Kalmanovich; Eran Nevo; Patricia Hersh

doi:https://doi.org/10.1090/proc/14380

On the cone of f-vectors of cubical polytopes

Ron M. Adin, Daniel Kalmanovich, Eran Nevo, Patricia Hersh

Bar-Ilan University, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

What is the minimal closed cone containing all f-vectors of cubical d-polytopes? We construct cubical polytopes showing that this cone, expressed in the cubical g-vector coordinates, contains the nonnegative g-orthant, thus verifying one direction of the Cubical Generalized Lower Bound Conjecture of Babson, Billera, and Chan. Our polytopes also show that a natural cubical analogue of the simplicial Generalized Lower Bound Theorem does not hold.

Original language	English
Pages (from-to)	1851-1866
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	5
DOIs	https://doi.org/10.1090/proc/14380
State	Published - 1 May 2019

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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On the cone of f-vectors of cubical polytopes

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