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

2010/06/10 by Marko Lindner, Lindner, Marko, Steffen Roch +1
Computer Science · Mathematics · #52B20 #52C07 #65J10 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Numerical Analysis (math.NA) #Point processes and geometric inequalities #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1006.2053

openalex publication_date 2010/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we compare the set of integer points in the homothetic copy\nn\Π of a lattice polytope \Π\⊆ R^d with the set of all sums\nx₁+\⋯+x_n with x₁,...,x_n\∈ \Π\∩ Z^d and n\∈ N. We give\nconditions on the polytope \Π under which these two sets coincide and we\ndiscuss two notions of boundary for subsets of Z^d or, more generally,\nsubsets of a finitely generated discrete group.\n

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