Séminaire Lotharingien de Combinatoire, 87B.4 (2023), 13 pp.

Stéphane Ouvry and Alexios P. Polychronakos

Signed area enumeration for lattice walks

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.

Received: October 19, 2021. Revised: April 14, 2023. Published: August 31, 2023.

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If you need to cite this article, here is a bibtex:

@article{OuvryPolychronakos23,
author = {Ouvry, St{\'e}phane and Polychronakos, Alexios P.},
title = {Signed area enumeration for lattice walks},
fjournal = {S{\'e}minaire Lotharingien de Combinatoire},
journal = {S{\'e}min. Lothar. Combin.},
issn={1286-4889},
volume = {87B},
number= {4},
pages = {1--13},
year = {2023},
language = {English},
doi={10.48550/arXiv.2110.09394},
}