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Lattice points in lattice polytopes

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  26 February 2010

Oleg Pikhurko
Oleg Pikhurko
Affiliation:
DPMMS, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB, England. E-mail: O.Pikhurko@dpmms.cam.ac.uk
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Abstract

It is shown that, for any lattice polytope P⊂ℝd the set int (P)∩lℤd (provided that it is non-empty) contains a point whose coefficient of asymmetry with respect to P is at most 8d · (8l+7)22d+1. If, moreover, P is a simplex, then this bound can be improved to 8 · (8l+7 )2d+1. As an application, new upper bounds on the volume of a lattice polytope are deduced, given its dimension and the number of sublattice points in its interior.

MSC classification

Secondary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)
Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 15 - 24
Copyright
Copyright © University College London 2001

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