Parking trees and the toric g-vector of nestohedra
Combinatorics
2026-03-17 v2
Abstract
We express the toric g-vector entries of any simple polytope as a nonnegative integer linear combination of its gamma-vector entries. We show that the toric g-vector of the associahedron is the ascent statistic of 123-avoiding parking functions. An analogous result holds for the cyclohedron and 123-avoiding functions. We prove that the toric g-vector of the permutahedron records the ascent statistics of parking trees representing 123-avoiding parking functions. We indicate how our approach extends to all chordal nestohedra.
Cite
@article{arxiv.2511.04815,
title = {Parking trees and the toric g-vector of nestohedra},
author = {Richard Ehrenborg and Gábor Hetyei and Margaret Readdy},
journal= {arXiv preprint arXiv:2511.04815},
year = {2026}
}
Comments
34 pages, 5 figures and 3 tables