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An involution for symmetry of hook length and part length of partitions
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math.CO
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lengthhookinvolutionlambdapartpartitionspointedbessenrodt
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abstract
A {\em pointed partition} of $n$ is a pair $(\lambda, v)$ where $\lambda\vdash n$ and $v$ is a cell in its Ferrers diagram. We construct an involution on pointed partitions of $n$ exchanging "hook length" and "part length". This gives a bijective proof of a recent result of Bessenrodt and Han.
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