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

Ehrenborg, Richard