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19972026
most citedEfficient Behavior of Small-World Networks

5.1k citations

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Showing 2021 · math-phShow all

3 papers · 2 filters

math-ph2021

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…

math-ph2021★ 5 cited

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…

math-ph2021★ 6 cited

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…