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arXiv · 2605.08968

Proofs of four generating function conjectures for arbor polytopes

Feihu Liu·Jinlong Tang
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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.

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Feihu Liu, Jinlong Tang. 2026-05-09. Proofs of four generating function conjectures for arbor polytopes. https://arxiv.org/abs/2605.08968

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