Proofs of four generating function conjectures for arbor polytopes
Combinatorics
2026-05-12 v1
Abstract
This paper proves four conjectured generating series, due to Chapoton, which concern invariants of posets and polytopes associated with a specific sequence of arbors. Two of these conjectures provide closed-form formulas for the generating series of the Zeta polynomial and the generating series of the M-triangle of the poset, respectively. The remaining two conjectures pertain, respectively, to the Ehrhart polynomial and the Laplace transform of the volume function of the associated arbor polytope.
Keywords
Cite
@article{arxiv.2605.08968,
title = {Proofs of four generating function conjectures for arbor polytopes},
author = {Feihu Liu and Jinlong Tang},
journal= {arXiv preprint arXiv:2605.08968},
year = {2026}
}