Li Gan 1 Stéphane Ouvry 1 Alexios P. Polychronakos 2, 3
Li Gan, Stéphane Ouvry, Alexios P. Polychronakos. Combinatorics of generalized Dyck and Motzkin paths. Phys.Rev.E, 2022, 106 (4), pp.044123. ⟨10.1103/PhysRevE.106.044123⟩. ⟨hal-03758544⟩
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.
- 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CCNY – City College of New York [CUNY]
- 3. CUNY – City University of New York [New York]