English

Signed area enumeration for lattice walks

Mathematical Physics 2023-12-01 v3 math.MP

Abstract

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 mechanics. Explicit combinatorial formulae are proposed which rely on sums labelled by the multicompositions of the length of the walks.

Cite

@article{arxiv.2110.09394,
  title  = {Signed area enumeration for lattice walks},
  author = {Stephane Ouvry and Alexios P. Polychronakos},
  journal= {arXiv preprint arXiv:2110.09394},
  year   = {2023}
}

Comments

Version published in S\'eminaire Lotharingien de Combinatoire; 13 pages, 4 figures

R2 v1 2026-06-24T06:58:49.707Z