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Hooks and powers of parts in partitions. (English) Zbl 1021.05008
Summary: 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 \(n\).

MSC:
05A17 Combinatorial aspects of partitions of integers
Keywords:
number of hooks
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