Year: 2026
Type: preprint
Abstract: Given a fence poset P , we define a new statistic on permutations, denoted by blP, that provides a combinatorial interpretation of the coefficients of the order polynomial of P , answering a question of Ferroni, Morales, and Panova (2025). Using the fact that the base polytope of a lattice path matroid can be decomposed into order polytopes of fence posets, we also obtain a combinatorial interpretation of the coefficients of the Ehrhart polynomial of the base polytope of Schubert matroids, answering a question of Stanley (1999). As an application of this statistic, we establish the first nontrivial lower bound for the linear coefficient of the Ehrhart polynomial of an order polytope. Finally, we conjecture generalizations of this statistic to skew-shape posets and circular fence posets.
Source: arXiv (Cornell University)
Author: Kahane, Yakob
Institution: Université du Québec à Montréal
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G373193047, G7107124846
OpenAlex ID: W7168264810