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- W2017675105 abstract "Given a polyhedral complex C with convex support, we characterize, by a local codimension-2 condition, polyhedral complexes that coarsen C. The proof of the characterization draws upon a surprising general shortcut for showing that a collection of polyhedra is a polyhedral complex and upon a property of hyperplane arrangements which is equivalent, for Coxeter arrangements, to Tits' solution to the Word Problem. The motivating special case, the case where C is a complete fan, generalizes a result of Morton, Pachter, Shiu, Sturmfels, and Wienand that equates convex rank tests with semigraphoids. The proof of the main result also implies a special case of Tietze's convexity theorem. We also prove oriented matroid versions of our results, obtaining, as a byproduct, an oriented matroid version of Tietze's convexity theorem." @default.
- W2017675105 created "2016-06-24" @default.
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- W2017675105 date "2012-10-01" @default.
- W2017675105 modified "2023-09-23" @default.
- W2017675105 title "Coarsening polyhedral complexes" @default.
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- W2017675105 doi "https://doi.org/10.1090/s0002-9939-2012-11194-3" @default.
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