Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/643
Title: Cyclohedron and Kantorovich–Rubinstein Polytopes
Authors: Jevtić, Filip D.
Jelić Milutinović, Marija 
Živaljević, Rade T.
Affiliations: Topology 
Keywords: Cyclohedron;Kantorovich-Rubinstein polytopes;Lipschitz polytope;Metric spaces;Nestohedron;Unimodular triangulations
Issue Date: 1-Apr-2018
Journal: Arnold Mathematical Journal
Abstract: 
We show that the cyclohedron (Bott–Taubes polytope) Wn arises as the polar dual of a Kantorovich–Rubinstein polytope KR(ρ) , where ρ is an explicitly described quasi-metric (asymmetric distance function) satisfying strict triangle inequality. From a broader perspective, this phenomenon illustrates the relationship between a nestohedron Δ F^ (associated to a building set F^) and its non-simple deformation Δ F, where F is an irredundant or tight basis of F^ (Definition 21). Among the consequences are a new proof of a recent result of Gordon and Petrov (Arnold Math. J. 3(2):205–218, 2017) about f-vectors of generic Kantorovich–Rubinstein polytopes and an extension of a theorem of Gelfand, Graev, and Postnikov, about triangulations of the type A, positive root polytopes.
URI: https://research.matf.bg.ac.rs/handle/123456789/643
ISSN: 21996792
DOI: 10.1007/s40598-018-0083-4
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