Robot Motion Planning
Lectures on Discrete Geometry
f-Vectors of Minkowski Additions of Convex Polytopes
Discrete & Computational Geometry
Stabilization of polytopic delay difference inclusions via the Razumikhin approach
Automatica (Journal of IFAC)
The maximum number of faces of the Minkowski sum of two convex polytopes
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The maximum number of faces of the minkowski sum of three convex polytopes
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We show that for polytopes P"1,P"2,...,P"r@?R^d, each having n"i=d+1 vertices, the Minkowski sum P"1+P"2+...+P"r cannot achieve the maximum of @?"in"i vertices if r=d. This complements a recent result of Fukuda and Weibel (2006), who show that this is possible for up to d-1 summands. The result is obtained by combining methods from discrete geometry (Gale transforms) and topological combinatorics (van Kampen-type obstructions).