Year: 2025
Type: article
Abstract: Starting from the data of an arbor, which is a rooted tree with vertices decorated by disjoint sets, we introduce a lattice polytope and a partial order on its lattice points. We give recursive formulas for various classical invariants of these polytopes and posets, using the tree structure. For linear arbors, we propose a conjecture exchanging the Ehrhart polynomial of the polytope with the Zeta polynomial of the poset for the reverse arbor. The general motivation comes from a transmutation operator acting on $M$-triangles, which should link the posets considered here with some kind of generalized noncrossing partitions and generalized associahedra. We give some evidence for this relationship in several cases, including notably some polytopes, namely halohedra and Hochschild polytopes.
Source: MATHEMATICA SCANDINAVICA
Author: Frédéric Chapoton
Institution: Institut de Recherche Mathématique Avancée
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4415313799
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