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Séminaire Lotharingien de Combinatoire, B47d (2002), 11 pp.

# Roland Bacher and Laurent Manivel

#
Hooks and Powers of Parts in Partitions

**Abstract.**
This paper shows that the number of hooks
of length *k* contained in all partitions of *n* equals *k*
times the
number of parts of length *k* in partitions of *n*. It contains also
formulas for the moments (under uniform distribution) of
*k*-th parts in partitions of *n*.

Received: September 27, 2001; Accepted: December 28, 2001; Final Version:
January 16, 2002.

The following versions are available: