Almost simplicial polytopes: The lower and upper bound theorems

Eran Nevo; Guillermo Pineda-Villavicencio; Julien Ugon; David Yost

Almost simplicial polytopes: The lower and upper bound theorems

Eran Nevo, Guillermo Pineda-Villavicencio, Julien Ugon, David Yost

Einstein Institute of Mathematics

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

Original language	English
Pages (from-to)	947-958
Number of pages	12
Journal	Discrete Mathematics and Theoretical Computer Science
State	Published - 2016
Event	28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada Duration: 4 Jul 2016 → 8 Jul 2016

Bibliographical note

Publisher Copyright:
© 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France

Keywords

F-vector
Graph rigidity
LBT
Moment curve
Polytope
UBT

Cite this

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AU - Pineda-Villavicencio, Guillermo

AU - Ugon, Julien

AU - Yost, David

PY - 2016

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N2 - This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

AB - This is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

KW - F-vector

KW - Graph rigidity

KW - LBT

KW - Moment curve

KW - Polytope

KW - UBT

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JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

Y2 - 4 July 2016 through 8 July 2016

ER -

Almost simplicial polytopes: The lower and upper bound theorems

Abstract

Bibliographical note

Keywords

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