Symmetry distribution between hook length and part length for partitions

Christine Bessenrodt (1) , Guo-Niu Han (2)

1 Hannover University
2 IRMA - Institut de Recherche Mathématique Avancée

It is known that the two statistics on integer partitions ``hook length" and ``part length" are equidistributed over the set of all partitions of $n$. We extend this result by proving that the bivariate joint generating function by those two statistics is symmetric. Our method is based on a generating function by a triple statistic much easier to calculate.

Domaines: Combinatoire [math.CO]

Christine Bessenrodt, Guo-Niu Han. Symmetry distribution between hook length and part length for partitions. Discrete Mathematics, 2009, 6 p. ⟨hal-00395700⟩