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math-ph2022★ 6 cited
Combinatorics of generalized Dyck and Motzkin paths
Li Gan, Stéphane Ouvry, Alexios P. Polychronakos
We relate the combinatorics of periodic generalized Dyck and Motzkin paths to the cluster coefficients of particles obeying generalized exclusion statistics, and obtain explicit ex…
math-ph2022★ 6 cited
Algebraic area enumeration for open lattice walks
Stephane Ouvry, Alexios Polychronakos
We calculate the number of open walks of fixed length and algebraic area on a square planar lattice by an extension of the operator method used for the enumeration of closed walks.…