Catalan-Spitzer permutations
Combinatorics
2023-10-11 v1
Abstract
We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to a generalization of results of Flajolet from continued fractions to continuants. The study of the other class leads to the discovery of a restricted variant of the Foata--Strehl group action.
Cite
@article{arxiv.2310.06288,
title = {Catalan-Spitzer permutations},
author = {Richard Ehrenborg and Gábor Hetyei and Margaret Readdy},
journal= {arXiv preprint arXiv:2310.06288},
year = {2023}
}