English

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