Catalan--Spitzer permutations
Richard Ehrenborg, G\'abor Hetyei, UNC Charlotte, Margaret Readdy · Enumerative Combinatorics and Applications · 2023
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.