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Coxeter submodular functions and deformations of Coxeter permutahedra

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sword-2021-05-26T11:59:03.original.xml (130 B)
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Author(s)
Ardila, Federico
•
Castillo, Federico
•
Eur, Christopher
•
Postnikov, Alexander
Date Issued
2020
Journal
Advances in Mathematics
Publisher
Elsevier BV
Version
Author's final manuscript
Abstract
© 2020 Elsevier Inc. We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This class of polytopes contains important families such as weight polytopes, signed graphic zonotopes, Coxeter matroids, root cones, and Coxeter associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids, and submodular functions to any finite reflection group.
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DOI of Published Version
10.1016/J.AIM.2020.107039
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