Séminaire Lotharingien de Combinatoire, 82B.98 (2019), 12 pp.

Federico Ardila, Federico Castillo, Christopher Eur, and Alex Postnikov

Deformations of Coxeter permutahedra and Coxeter submodular functions

Abstract. We study the cone of deformations of a Coxeter permutahedron. This family contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra and submodular functions to any finite reflection group.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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