Minkowski sum of polytopes and its normality

2013/12/22 by Akihiro Higashitani, Higashitani, Akihiro
Mathematics · #13F99 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Metric Geometry (math.MG) #Primary 52B20 #Secondary 14M25 #math.AC #math.CO #math.MG #msc:13F99 #msc:14M25 #msc:52B20

paper · pdf · doi:10.48550/arxiv.1312.6340

14 pages, 3 figures, I welcome many comments

arxiv created 2014/07/17 · arxiv updated 2014/07/18

Abstract

In this paper, we consider the normality or the integer decomposition property (IDP, for short) for Minkowski sums of integral convex polytopes. We discuss some properties on the toric rings associated with Minkowski sums of integral convex polytopes. We also study Minkowski sums of edge polytopes and give a sufficient condition for Minkowski sums of edge polytopes to have IDP.

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