A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Steven Klee; Eran Nevo; Isabella Novik; Hailun Zheng

doi:10.1007/s00454-018-9978-z

A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Steven Klee, Eran Nevo, Isabella Novik^*, Hailun Zheng

^*Corresponding author for this work

Einstein Institute of Mathematics

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

7 Scopus citations

Abstract

Stanley proved that for any centrally symmetric simplicial d-polytope P with d≥ 3 , g2(P)≥(d2)-d. We provide a characterization of centrally symmetric simplicial d-polytopes with d≥ 4 that satisfy this inequality as equality. This gives a natural generalization of the classical Lower Bound Theorem for simplicial polytopes to the setting of centrally symmetric simplicial polytopes.

Original language	English
Pages (from-to)	541-561
Number of pages	21
Journal	Discrete and Computational Geometry
Volume	61
Issue number	3
DOIs	https://doi.org/10.1007/s00454-018-9978-z
State	Published - 15 Apr 2019

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Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Centrally symmetric polytopes
Face numbers
Infinitesimal rigidity
Missing faces
Stacked spheres
Stresses

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10.1007/s00454-018-9978-z

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AU - Nevo, Eran

AU - Novik, Isabella

AU - Zheng, Hailun

PY - 2019/4/15

Y1 - 2019/4/15

N2 - Stanley proved that for any centrally symmetric simplicial d-polytope P with d≥ 3 , g2(P)≥(d2)-d. We provide a characterization of centrally symmetric simplicial d-polytopes with d≥ 4 that satisfy this inequality as equality. This gives a natural generalization of the classical Lower Bound Theorem for simplicial polytopes to the setting of centrally symmetric simplicial polytopes.

AB - Stanley proved that for any centrally symmetric simplicial d-polytope P with d≥ 3 , g2(P)≥(d2)-d. We provide a characterization of centrally symmetric simplicial d-polytopes with d≥ 4 that satisfy this inequality as equality. This gives a natural generalization of the classical Lower Bound Theorem for simplicial polytopes to the setting of centrally symmetric simplicial polytopes.

KW - Centrally symmetric polytopes

KW - Face numbers

KW - Infinitesimal rigidity

KW - Missing faces

KW - Stacked spheres

KW - Stresses

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 3

ER -

A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Abstract

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Keywords

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