\magnification=1200\nopagenumbers\noindent
{\bf Hook lengths in a skew Young diagram}
\smallskip\noindent
{\bf Svante Janson}
\vskip1cm
\noindent Regev and Vershik
(Electronic J. Combinatorics {\bf4} (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.
\noindent We give a simple inductive proof of this
 conjecture.
\noindent Very recently, Regev and Zeilberger
(Annals of Combinatorics, to appear)
have independently proved this conjecture.


\end