Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers
@article{Ouvry2020LatticeWA, title={Lattice walk area combinatorics, some remarkable trigonometric sums and Ap{\'e}ry-like numbers}, author={St'ephane Ouvry and Alexios P. Polychronakos}, journal={Nuclear Physics}, year={2020}, volume={960}, pages={115174} }
7 Citations
Algebraic area enumeration of random walks on the honeycomb lattice.
- MathematicsPhysical review. E
- 2022
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 the problem to a…
A shifted binomial theorem and trigonometric series
- Mathematics
- 2020
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. Motivated by the…
Algebraic area enumeration for lattice paths
- Mathematics
- 2021
We give a summary of recent progress on the algebraic area enumeration of closed paths on planar lattices. Several connections are made with quantum mechanics and statistical mechanics. Explicit…
Hamiltonian and exclusion statistics approach to discrete forward-moving paths.
- MathematicsPhysical review. E
- 2021
This work expresses the length and area generating function for paths with arbitrary starting and ending points in terms of grand partition functions for exclusion particles in a finite harmonic spectrum and presents an alternative, simpler form for its logarithm that makes its polynomial structure explicit.
Length and area generating functions for height-restricted Motzkin meanders.
- MathematicsPhysical review. E
- 2022
We derive the length and area generating function of planar height-restricted forward-moving discrete paths of increments ±1 or 0 with arbitrary starting and ending points, the so-called Motzkin…
Algebraic area enumeration for open lattice walks
- Mathematics
- 2022
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. The open walk area…
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