Integer decomposition property of free sums of convex polytopes

2014/03/30 by Takayuki Hibi, Hibi, Takayuki, Akihiro Higashitani +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Analytic Number Theory Research #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Point processes and geometric inequalities #Primary 52B20 #Secondary 13P10 #math.AC #math.CO #msc:13P10 #msc:52B20

paper · pdf · doi:10.48550/arxiv.1403.7787

7 pages

openalex publication_date 2014/03/30 · arxiv created 2014/10/20 · arxiv updated 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P ⊂ ℝ^d and Q ⊂ ℝ^e be integral convex polytopes of dimension d and e which contain the origin of ℝ^d and ℝ^e, respectively. In the present paper, under some assumptions, the necessary and sufficient condition for the free sum of P and Q to possess the integer decomposition property will be presented.

Citations

• Chain polytopes and algebras with straightening laws

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