Maximal f-vectors of Minkowski sums of large numbers of polytopes

DOI10.1007/s00454-011-9385-1zbMath1243.52007OpenAlexW1650958023MaRDI QIDQ411394

Christophe Weibel

Publication date: 4 April 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-011-9385-1

zbMATH Keywords

polytopesMinkowski sumsf-vectors

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05)

Related Items (8)

Sharp Bounds for the Number of Regions of Maxout Networks and Vertices of Minkowski Sums ⋮ A worst-case optimal algorithm to compute the Minkowski sum of convex polytopes ⋮ The maximum number of faces of the Minkowski sum of two convex polytopes ⋮ A worst-case optimal algorithm to compute the Minkowski sum of convex polytopes ⋮ Relative Stanley-Reisner theory and upper bound theorems for Minkowski sums ⋮ A geometric approach for the upper bound theorem for Minkowski sums of convex polytopes ⋮ The convex dimension of hypergraphs and the hypersimplicial Van Kampen-Flores theorem ⋮ On the exact maximum complexity of Minkowski sums of polytopes

Cites Work

• The maximum number of faces of the Minkowski sum of two convex polytopes
• A linear equation for Minkowski sums of polytopes relatively in general position
• Topological obstructions for vertex numbers of Minkowski sums
• On overlays and minimization diagrams
• On the exact maximum complexity of Minkowski sums of polytopes
• \(f\)-vectors of Minkowski additions of convex polytopes
• Partially Observable Markov Decision Processes: A Geometric Technique and Analysis
• Lectures on Polytopes
• Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Bases
• Algebraic Statistics for Computational Biology

This page was built for publication: Maximal f-vectors of Minkowski sums of large numbers of polytopes