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.
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