The Lower Bound Theorem for polytopes that approximate C1-convex bodies

Karim Adiprasito; José Alejandro Samper

The Lower Bound Theorem for polytopes that approximate C¹-convex bodies

Karim Adiprasito, José Alejandro Samper

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

Abstract

The face numbers of simplicial polytopes that approximate C¹-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence {Pn}⁸_n=0 of simplicial polytopes converges to a C¹-convex body in the Hausdorff distance, then the entries of the g-vector of Pn converge to infinity.

Original language	English
Pages (from-to)	277-287
Number of pages	11
Journal	Discrete Mathematics and Theoretical Computer Science
State	Published - 2014
Externally published	Yes
Event	26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States Duration: 29 Jun 2014 → 3 Jul 2014

Bibliographical note

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

Keywords

Approximation theory
Convex bodies
F-vector theory
Geometric Combinatorics
Lower bound theorem
Polytopes

Cite this

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title = "The Lower Bound Theorem for polytopes that approximate C1-convex bodies",

abstract = "The face numbers of simplicial polytopes that approximate C1-convex bodies in the Hausdorff metric is studied. Several structural results about the skeleta of such polytopes are studied and used to derive a lower bound theorem for this class of polytopes. This partially resolves a conjecture made by Kalai in 1994: if a sequence {Pn}8n=0 of simplicial polytopes converges to a C1-convex body in the Hausdorff distance, then the entries of the g-vector of Pn converge to infinity.",

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KW - Convex bodies

KW - F-vector theory

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Y2 - 29 June 2014 through 3 July 2014

ER -

The Lower Bound Theorem for polytopes that approximate C¹-convex bodies

Abstract

Bibliographical note

Keywords

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