Coxeter submodular functions and deformations of Coxeter permutahedra

Alexander Postnikov; Christopher Eur; Federico Ardila; Federico Castillo

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Coxeter submodular functions and deformations of Coxeter permutahedra

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arxiv 1904.11029 v2 pith:T57TDFWB submitted 2019-04-24 math.CO

Federico Ardila , Federico Castillo , Christopher Eur , Alexander Postnikov This is my paper

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keywords coxeterconedeformationsfunctionspermutahedrasubmodularanalogsassociahedra

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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 family of polytopes contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids, and submodular functions to any finite reflection group.

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