An involution for symmetry of hook length and part length of partitions

Heesung Shin; Jiang Zeng

doi:10.1016/j.disc.2010.01.011

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arXiv · 0907.4880

An involution for symmetry of hook length and part length of partitions

Heesung Shin·Jiang Zeng

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Abstract

A {\em pointed partition} of $n$ is a pair $(λ, v)$ where $λ\vdash n$ 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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Heesung Shin, Jiang Zeng. 2009-10-07. An involution for symmetry of hook length and part length of partitions. https://doi.org/10.1016/j.disc.2010.01.011

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