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THE BOUNDARY VOLUME OF A LATTICE POLYTOPE

Published online by Cambridge University Press:  26 September 2011

GÁBOR HEGEDÜS
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, A-4040 Linz, Austria (email: gabor.hegedues@oeaw.ac.at)
ALEXANDER M. KASPRZYK*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom (email: a.m.kasprzyk@imperial.ac.uk)
*
For correspondence; e-mail: a.m.kasprzyk@imperial.ac.uk
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Abstract

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For a d-dimensional convex lattice polytope P, a formula for the boundary volume vol(∂P) is derived in terms of the number of boundary lattice points on the first ⌊d/2⌋ dilations of P. As an application we give a necessary and sufficient condition for a polytope to be reflexive, and derive formulas for the f-vector of a smooth polytope in dimensions three, four, and five. We also give applications to reflexive order polytopes, and to the Birkhoff polytope.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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