A note on Kalai's $3^d$ Conjecture

Gregory R. Chambers; Elia Portnoy

A note on Kalai's $3^d$ Conjecture

Combinatorics 2023-08-08 v2 Differential Geometry

Authors: Gregory R. Chambers , Elia Portnoy

Abstract

Suppose that $C$ is a centrally symmetric $d$ -dimensional convex polytope; in 1989 Kalai conjectured that $C$ has at least $3^d$ facets. We prove this result if there are $d$ hyperplanes with orthogonal normal vectors so that $C$ is symmetric about all of them.

Keywords

polytopes convex geometry

Cite

@article{arxiv.2211.09215,
  title  = {A note on Kalai's $3^d$ Conjecture},
  author = {Gregory R. Chambers and Elia Portnoy},
  journal= {arXiv preprint arXiv:2211.09215},
  year   = {2023}
}

Comments

4 pages

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