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

Karim Adiprasito, José Alejandro Samper

Research output: Contribution to journalConference articlepeer-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}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.

Original languageEnglish (US)
Pages (from-to)277-287
Number of pages11
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2014
Externally publishedYes
Event26th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2014 - Chicago, United States
Duration: Jun 29 2014Jul 3 2014

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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