Permutohedron's volume via Dyck paths
Combinatorics
2025-04-01 v1
Abstract
In a recent project, Castillo, Libedinsky, Plaza, and the author established a deep connection between the size of lower Bruhat intervals in affine Weyl groups and the volume of the permutohedron, showing that the former can be expressed as a linear combination of the latter. In this paper, we provide a formula for the volume of this polytope in terms of Dyck paths. Thus, we present a shorter, alternative, and enlightening proof of a previous formula given by Postnikov.
Keywords
Cite
@article{arxiv.2503.23122,
title = {Permutohedron's volume via Dyck paths},
author = {Damian de la Fuente},
journal= {arXiv preprint arXiv:2503.23122},
year = {2025}
}
Comments
11 pages