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Ehrhart Polynomials and Successive Minima

Published online by Cambridge University Press:  21 December 2009

Martin Henk
Universität Magdeburg, IAG, Universitätsplatz 2, D-39106 Magdeburg, Germany. E-Mail:
Achill Schürmann
Universität Magdeburg, Institut für Algebra und Geometrie, Universitätsplatz 2, D-39106 Magdeburg, Germany. E-mail:
Jörg M. Wills
Universität Siegen, Mathematisches Institut, ENC, D-57068 Siegen, Germany. E-mail:


The Ehrhart polynomials for the class of 0-symmetric convex lattice polytopes in Euclidean n-space ℝn are investigated. It turns out that the roots of the Ehrhart polynomial and Minkowski's successive minima of such polytopes are closely related by their geometric and arithmetic means. It is also shown that the roots of the Ehrhart polynomials of lattice n-polytopes with or without interior lattice points differ essentially. Furthermore, the structure of the roots in the planar case is studied. Here it turns out that their distribution reflects basic properties of lattice polygons.

Research Article
Copyright © University College London 2005

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