Dyck paths and a bijection for multisets of hook numbers

Abstract

We give a bijective proof of a conjecture of Regev and Vershik on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection proves a result that is stronger and more symmetric than the original conjecture, by means of a construction involving Dyck paths, a particular type of lattice path.

10 pages, 4 figures