|Title:||Cyclohedron and Kantorovich–Rubinstein Polytopes||Journal:||Arnold Mathematical Journal||Volume:||4||Issue:||1||First page:||87||Last page:||112||Issue Date:||1-Apr-2018||ISSN:||2199-6792||DOI:||10.1007/s40598-018-0083-4||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.
|Keywords:||Cyclohedron | Kantorovich-Rubinstein polytopes | Lipschitz polytope | Metric spaces | Nestohedron | Unimodular triangulations||Publisher:||Springer Link||Project:||Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems
Topology, geometry and global analysis on manifolds and discrete structures
Show full item record
checked on Mar 20, 2023
checked on Mar 21, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.