Karim Adiprasito ; José Alejandro Samper - Polytopes and $C^1$-convex bodies

dmtcs:2399 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2399
Polytopes and $C^1$-convex bodies

Authors: Karim Adiprasito 1; José Alejandro Samper 2

  • 1 Institut des Hautes Études Scientifiques
  • 2 University of Washington [Seattle]

The face numbers of simplicial polytopes that approximate $C^1$-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 $\{P_n\}_{n=0}^{\infty}$ of simplicial polytopes converges to a $C^1$-convex body in the Hausdorff distance, then the entries of the $g$-vector of $P_n$ converge to infinity.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: convex bodies,Lower bound theorem,Approximation theory,Polytopes,f-vector theory,Geometric Combinatorics,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Around the theory of f-vectors; Funder: National Science Foundation; Code: 1069298

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