A linear equation for Minkowski sums of polytopes relatively in general position

Authors:
Komei Fukuda;Christophe Weibel
Affiliations:
Mathematics Institute, EPFL, Lausanne, Switzerland;Department of Mathematics, McGill University, Montreal, Canada
Venue:
European Journal of Combinatorics
Year:
2010

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Abstract

The objective of this paper is to study a special family of Minkowski sums, that is of polytopes relatively in general position. We show that the maximum number of faces in the sum can be attained by this family. We present a new linear equation that is satisfied by f-vectors of the sum and the summands. We study some of the implications of this equation.