Integer decomposition property of free sums of convex polytopes

Abstract

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

7 pages

References in corpus (1)

• Chain polytopes and algebras with straightening laws