Dyck paths and a bijection for multisets of hook numbers Original Research Article

We give a bijective proof of a result of Regev and Vershik (Electron J. Combin. 4 (1997) R22) on the equality of two multisets of hook numbers of certain skew–Young diagrams. The bijection is given in terms of Dyck paths, a particular type of lattice path. It is extended to also prove a recent, more refined result of Regev (European J. Combin. 21 (2000) 959), which concerns a special class of skew diagrams.