On Arnold's Problem on the Classifications of Convex Lattice Polytopes
Abstract
In 1980, V.I. Arnold studied the classification problem for convex lattice polygons of given area. Since then this problem and its analogues have been studied by B'ar'any, Pach, Vershik, Liu, Zong and others. Upper bounds for the numbers of nonequivalent ddimensional convex lattice polytopes of given volume or cardinality have been achieved. In this paper, by introducing and studying the unimodular groups acting on convex lattice polytopes, we obtain lower bounds for the number of nonequivalent ddimensional convex lattice polytopes of bounded volume or given cardinality, which are essentially tight.
 Publication:

arXiv eprints
 Pub Date:
 July 2011
 arXiv:
 arXiv:1107.2966
 Bibcode:
 2011arXiv1107.2966Z
 Keywords:

 Mathematics  Metric Geometry;
 52B20;
 52C07
 EPrint:
 15 pages, 3 figures