All Items 1 Collection 1 The Octagon 1 Contributor 4 Cox, David A. (Department of Mathematics and Statistics, Amherst College) 1 Haase, Christian (Institut fur Mathematik, Free University of Berlin) 1 Hibi, Takayuki (Department of Pure and Applied Mathematics, Osaka University) 1 Higashitani, Akihiro (Department of Mathematics, Kyoto University) 1 Topic 1 Applied mathematics 1 Part Of 1 The Amherst College Octagon 1 Genre 1 Articles 1 Subject 1 Applied mathematics 1 Integer decomposition property of dilated polytopes Cox, David A. (Department of Mathematics and Statistics, Amherst College) An integral convex polytope P in R^N possesses the integer decomposition property if, for any integer k > 0 and for any integer point a in kP, there exist integer points a_1,...,a_k in P such that a = a_1 + ... + a_k. A fundamental question is to determine the integers k > 0 for which the dilated polytope kP possesses the integer decomposition property. In the present paper, combinatorial invariants related to the integer decomposition property of dilated polytopes will be proposed and studied. Integer decomposition property of dilated polytopes