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Computing the Minkowski Sum of Prisms

Authors:	D. Pallaschke J. Rosenmüller

Affiliation:	1. Institut für Statistik und Mathem. Wirtschaftstheorie, Universit?t Karlsruhe, D-76128, Karlsruhe, Germany 2. Institut für Mathematische Wirtschaftsforschung, Universit?t Bielefeld, D-33615, Bielefeld, Germany

Abstract:	Within this paper we study the Minkowski sum of prisms (“Cephoids”) in a finite dimensional vector space. For a vector $a in mathbb{R}^n$ with positive components we write ${bar{a}} = ({1over bar{a}_1}, cdots , {1over bar{a}_n})$ and denote by $prod = prod^{bar{a}} = {x in mathbb{R}^n \| langle bar{a}, {bf x} rangle leqslant 1, {bf x} geqslant 0 }$ the associated prism. We provide a representation of a finite sum of prisms in terms of inequalities. Dedicated to the 65th birthday of Alexander Rubinov.

Keywords:	convex analysis minkowski sum polytopes
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