A combinatorial proof of the supper symmetric property of hook length

Abstract

There are $k$ kinds of length $k$ hooks with different arm length. Actually, this $k$ kinds appear uniformly in Young diagrams of size $n$. The property ``appear uniformly'' is called super symmetric. We give a combinatorial proof of the supper symmetric property of hook length.

This is the content already on C. Bessenrodt, `On hooks of Young diagrams', Annals of Comb. 2 (1998) 103-110