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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
number of hooks
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