Coxeter submodular functions and deformations of Coxeter permutahedra
Combinatorics
2020-03-03 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1904.11029,
title = {Coxeter submodular functions and deformations of Coxeter permutahedra},
author = {Federico Ardila and Federico Castillo and Christopher Eur and Alexander Postnikov},
journal= {arXiv preprint arXiv:1904.11029},
year = {2020}
}
Comments
Minor edits. To appear in Advances of Mathematics