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On the integer points in a lattice polytope: n-fold Minkowski sum and boundary

  • Marko LindnerEmail author
  • Steffen Roch
Original Paper

Abstract

In this article we compare the set of integer points in the homothetic copy \({n\Pi}\) of a lattice polytope \({\Pi\subseteq{{\mathbb R}}^d}\) with the set of all sums x 1 + . . . + x n with \({x_1,\ldots,x_n\in \Pi\cap{{\mathbb Z}}^d}\) and \({n\in{{\mathbb N}}}\) . We give conditions on the polytope \({\Pi}\) under which these two sets coincide and we discuss two notions of boundary for subsets of \({{{\mathbb Z}}^d}\) or, more generally, subsets of a finitely generated discrete group.

Keywords

Lattice polytopes Integer points Boundary Projection methods 

Mathematics Subject Classification (2000)

52B20 52C07 65J10 

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Copyright information

© The Managing Editors 2011

Authors and Affiliations

  1. 1.Fakultät MathematikTU ChemnitzChemnitzGermany
  2. 2.TU Bergakademie Freiberg, Fakultät für Mathematik und Informatik, Institut für Angewandte AnalysisFreibergGermany
  3. 3.Fachbereich MathematikTU DarmstadtDarmstadtGermany

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