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On the Number of Lattice Free Polytopes

✍ Scribed by Imre Bárány; Jean-Michel Kantor

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
110 KB
Volume
21
Category
Article
ISSN
0195-6698

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✦ Synopsis

asked for estimates for the number of equivalence classes of lattice polytopes, under the group of unimodular affine transformations. What we investigate here is the analogous question for lattice free polytopes. Some of the results: the number of equivalence classes of lattice free simplices of volume at most v in dimension d is of order v d-1 , and the number of equivalence classes of lattice free polytopes of volume at most v in dimension d is O(v 2 d -1 (log v) d-2 ).

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