Hooks and Powers of Parts in Partitions
Séminaire lotharingien de combinatoire, Tome 47 (2001-2002)
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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.
@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/}
}
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/