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The polytope-collision problem
Published 2017“…Recently, it was shown that the problem is decidable for vector-space targets of dimension at most three, followed by another development showing that the problem is in PSPACE for polytope targets of dimension at most three. In this work, we take a dual look at the problem, and consider the case where the initial vector $x$ is replaced with a polytope $P_1$, and the target is a polytope $P_2$. …”
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Scale-isometric polytopal graphs in hypercubes and cubic lattices : polytopes in hypercubes and Zn /
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A Special Role of Boolean Quadratic Polytopes among Other Combinatorial Polytopes
Published 2016-02-01“…For comparing two families of polytopes we use the following method. We say that a family…”
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The Gomory-Chvátal closure of a non-rational polytope is a rational polytope
Published 2013“…The question as to whether the Gomory-Chvátal closure of a nonrational polytope is a polytope has been a longstanding open problem in integer programming. …”
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Enumerating Triangulations of Convex Polytopes
Published 2001-01-01Subjects: “…polytope…”
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Delannoy numbers and Legendre polytopes
Published 2008-01-01Subjects: “…centrally symmetric polytopes…”
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Tsirelson Polytopes and randomness generation
Published 2020-01-01“…We classify the extreme points of a polytope of probability distributions in the (2,2,2) CHSH-Bell setting that is induced by a single Tsirelson bound. …”
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The Thermomajorization Polytope and Its Degeneracies
Published 2024-01-01“…Moreover, using a geometric approach by studying the so-called thermomajorization polytope, we prove that any subspace in equilibrium can be brought out of equilibrium via thermal operations. …”
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Polytopes from Subgraph Statistics
Published 2011-01-01Subjects: “…polytopes…”
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Defining amplituhedra and Grassmann polytopes
Published 2020-04-01“…Lam (2015) gave a sufficient condition for the induced map Gr≥0 k,n → Grk,r to be well defined, in which case he called the image a Grassmann polytope. (In the case k = 1, Grassmann polytopes are just polytopes, and amplituhedra are cyclic polytopes.) …”
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Cutting convex polytopes by hyperplanes
Published 2020“…Cutting a polytope is a very natural way to produce new classes of interesting polytopes. …”
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