On an involution on the Dyck paths
In the paper [J. Comb. Theory, Ser. A 60, 225-245 (1992; Zbl 0754.05033)], the author gave two interpretations of certain generating functions which have simple expressions in terms of \(q\)-Bessel functions- --one in terms of multi-walks over binary trees and the other in terms of multichains over Dyck paths. By defining an involution on the set \(D\) of paths of Dyck and bijections between paths and multi-walks and between paths and multichains, the author gives a bijective proof of the equivalence of the two interpretations.
scientific article; zbMATH DE number 438332