English

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}
}
R2 v1 2026-06-28T12:45:28.148Z