440 citations · 4.5k across the 106 of their papers we have counts for
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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…
Length and area generating functions for height-restricted Motzkin meanders
Alexios P. Polychronakos
We derive the length and area generating function of planar height-restricted forward-moving discrete paths of increments +1, 0, or -1 with arbitrary starting and ending points, th…
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…