Geodesic
Hooks and Powers of Parts in Partitions
Séminaire lotharingien de combinatoire, Tome 47 (2001-2002) 
Roland Bacher; Laurent Manivel. Hooks and Powers of Parts in Partitions. Séminaire lotharingien de combinatoire, Tome 47 (2001-2002). http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a3/
@article{SLC_2001-2002_47_a3,
     author = {Roland Bacher and Laurent Manivel},
     title = {Hooks and {Powers} of {Parts} in {Partitions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2001-2002},
     volume = {47},
     url = {http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a3/}
}
TY  - JOUR
AU  - Roland Bacher
AU  - Laurent Manivel
TI  - Hooks and Powers of Parts in Partitions
JO  - Séminaire lotharingien de combinatoire
PY  - 2001-2002
VL  - 47
UR  - http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a3/
ID  - SLC_2001-2002_47_a3
ER  - 
%0 Journal Article
%A Roland Bacher
%A Laurent Manivel
%T Hooks and Powers of Parts in Partitions
%J Séminaire lotharingien de combinatoire
%D 2001-2002
%V 47
%U http://geodesic.mathdoc.fr/item/SLC_2001-2002_47_a3/
%F SLC_2001-2002_47_a3

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

This paper shows that the number of hooks of length k contained in all partitions of n equals k times the number of parts of length k in partitions of n. It contains also formulas for the moments (under uniform distribution) of k-th parts in partitions of n.