Combinatorics of generalized Dyck and Motzkin paths
Mathematical Physics
2022-10-17 v1 Statistical Mechanics
High Energy Physics - Theory
Combinatorics
math.MP
Abstract
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficients of particles obeying generalized exclusion statistics, and obtain explicit expressions for the counting of paths with a fixed number of steps of each kind at each vertical coordinate. A class of generalized compositions of the integer path length emerges in the analysis.
Keywords
Cite
@article{arxiv.2207.07664,
title = {Combinatorics of generalized Dyck and Motzkin paths},
author = {Li Gan and Stéphane Ouvry and Alexios P. Polychronakos},
journal= {arXiv preprint arXiv:2207.07664},
year = {2022}
}
Comments
27 pages, 11 figures