Combinatorics of generalized Dyck and Motzkin paths – Archive ouverte HAL

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]