32 citations · 494 across the 64 of their papers we have counts for
17 papers · 1 filter
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…
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.…
Signed area enumeration for lattice walks
Stephane Ouvry, Alexios P. Polychronakos
We give a summary of recent progress on the signed area enumeration of closed walks on planar lattices. Several connections are made with quantum mechanics and statistical mechanic…
Algebraic area enumeration of random walks on the honeycomb lattice
Li Gan, Stéphane Ouvry, Alexios P. Polychronakos
We study the enumeration of closed walks of given length and algebraic area on the honeycomb lattice. Using an irreducible operator realization of honeycomb lattice moves, we map t…
Hamiltonian and exclusion statistics approach to discrete forward-moving paths
Stéphane Ouvry, Alexios P. Polychronakos
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propag…
A shifted binomial theorem and trigonometric series
Stéphane Ouvry, Alexios P. Polychronakos
We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums.…