Hook lengths in a skew Young diagram
Regev and Vershik (Electronic J. Combinatorics 4 (1997), #R22) have obtained some properties of the set of hook lengths for certain skew Young diagrams, using asymptotic calculations of character degrees. They also conjectured a stronger form of one of their results.
We give a simple inductive proof of this conjecture.
Very recently, Regev and Zeilberger (Annals of Combinatorics, to appear) have independently proved this conjecture.