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

Heesung Shin, Jiang Zeng

Published 2009-07-28, updated 2009-10-07Version 2

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.