Acta Mathematica Hungarica
Volume/Issue:
Volume 137: Issue 1-2
On a question of V. I. Arnol'd
Author: Imre Bárány 1 , 2
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  • 1 Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest, Pf. 127, Hungary
  • 2 Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
DOI:
https://doi.org/10.1007/s10474-012-0219-2
Page Count:
72–81
Publication Date:
01 Oct 2012
Online Publication Date:
27 Apr 2012
Article Category:
Research Article
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Abstract

We show by a construction that there are at least exp {cV(d−1)/(d+1)} convex lattice polytopes in ℝd of volume V that are different in the sense that none of them can be carried to an other one by a lattice preserving affine transformation.

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  • [3] Bárány, I. 2008 Random points and lattice points in convex bodies Bull. Amer. Math. Soc. 45 339–365 .

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  • [8] Reizner, Sh. Schütt, C. Werner, E. 2001 Dropping a vertex or a facet from a convex polytope Forum Mathematicum 13 359–378 .

  • [9] Zong, C., On Arnold's problem on the classifications of convex lattice polytopes, manuscript (2011), arXiv:1107.2966 http://arxiv.org/abs/1107.2966.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632
Keywords:
lattice; polytope; integer convex hull; statistics of convex lattice polytopes; 52B20; 11H06

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