Algebra and Combinatorics of the Brion map on Generalized Permutahedra
Combinatorics
2025-12-02 v2
Abstract
The Brion morphism maps a generalized permutahedron to a collection of posets associated to its vertices. We compute this map explicitly for the Hopf monoids of permutahedra, associahedra, and orbit polytopes, and we explore the dual Brion map of the primitive Lie monoids associated to these three Hopf monoids. We describe the Lie monoid structure of the primitives in this dual setting and in particular we show that the Lie monoid of primitives of associahedra is isomorphic to the positive part of the Witt Lie algebra
Keywords
Cite
@article{arxiv.2310.09900,
title = {Algebra and Combinatorics of the Brion map on Generalized Permutahedra},
author = {Alvaro Cornejo and Mariel Supina},
journal= {arXiv preprint arXiv:2310.09900},
year = {2025}
}
Comments
27 pages, 14 figures; Major revisions to introduction and background