Polygons as sections of higher-dimensional polytopes

zbMath1312.52008arXiv1404.2443MaRDI QIDQ2256121

Julian Pfeifle, Arnau Padrol

Publication date: 19 February 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.2443

zbMATH Keywords

polygonextension complexitynonnegative ranknonrealizabilitypseudo-line arrangementspolytope projecions and section

Mathematics Subject Classification ID

Factorization of matrices (15A23) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Polytopes and polyhedra (52B99)

Related Items (8)

Heuristics for exact nonnegative matrix factorization ⋮ A separation between tropical matrix ranks ⋮ Extension complexity of low-dimensional polytopes ⋮ Euclidean distance matrices and separations in communication complexity theory ⋮ Extension complexity and realization spaces of hypersimplices ⋮ Hidden vertices in extensions of polytopes ⋮ Extension Complexity of Polytopes with Few Vertices or Facets ⋮ Tropical lower bound for extended formulations. II. Deficiency graphs of matrices

Cites Work

• Extended formulations for polygons
• Worst-case results for positive semidefinite rank
• Real rank versus nonnegative rank
• Expressing combinatorial optimization problems by linear programs
• An upper bound for nonnegative rank
• Detecting matrices of combinatorial rank three
• Stochastic factorizations, sandwiched simplices and the topology of the space of explanations
• Lifts of Convex Sets and Cone Factorizations
• On Polyhedral Approximations of the Second-Order Cone

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