On Ranks of Regular Polygons

DOI10.1137/16M1105608zbMath1384.52004arXiv1610.09868MaRDI QIDQ4594484

Pedro M. Silva, João Gouveia, António Pedro Goucha

Publication date: 24 November 2017

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.09868

zbMATH Keywords

Boolean rankpolygonsnonnegative ranksemidefinite rank

Mathematics Subject Classification ID

Factorization of matrices (15A23) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05)

Related Items (5)

Complex psd-minimal polytopes in dimensions two and three ⋮ The Phaseless Rank of a Matrix ⋮ Optimal Size of Linear Matrix Inequalities in Semidefinite Approaches to Polynomial Optimization ⋮ Algorithms for positive semidefinite factorization ⋮ Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

Cites Work

• Heuristics for exact nonnegative matrix factorization
• Polytopes of minimum positive semidefinite rank
• Four-dimensional polytopes of minimum positive semidefinite rank
• On the linear extension complexity of regular \(n\)-gons
• Non-projectability of polytope skeleta
• Extended formulations for polygons
• Worst-case results for positive semidefinite rank
• On the geometric interpretation of the nonnegative rank
• On a unimodal sequence of binomial coefficients
• An upper bound for nonnegative rank
• Which nonnegative matrices are slack matrices?
• Exponential Lower Bounds for Polytopes in Combinatorial Optimization
• Lower Bounds on the Size of Semidefinite Programming Relaxations
• The Matching Polytope has Exponential Extension Complexity
• Lifts of Convex Sets and Cone Factorizations
• Constructing Extended Formulations from Reflection Relations
• The maximum numbers of faces of a convex polytope
• On Polyhedral Approximations of the Second-Order Cone
• Unnamed Item

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