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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