A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Steven Klee; Eran Nevo; Isabella Novik; Hailun Zheng

doi:https://doi.org/10.1007/s00454-018-9978-z

A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Steven Klee, Eran Nevo, Isabella Novik, Hailun Zheng

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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	American 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

Keywords

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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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https://doi.org/10.1007/s00454-018-9978-z

Cite this

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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.",

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AU - Klee, Steven

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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U2 - https://doi.org/10.1007/s00454-018-9978-z

DO - https://doi.org/10.1007/s00454-018-9978-z

M3 - Article

SN - 0179-5376

VL - 61

SP - 541

EP - 561

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 3

ER -

A Lower Bound Theorem for Centrally Symmetric Simplicial Polytopes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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