• Corpus ID: 15137279

# Hooks and powers of parts in partitions

@article{Bacher2001HooksAP,
title={Hooks and powers of parts in partitions},
author={Roland Bacher and Laurent Manivel},
journal={S{\'e}minaire Lotharingien de Combinatoire},
year={2001},
volume={47},
pages={11}
}
• Published 29 August 2001
• Mathematics
• Séminaire Lotharingien de Combinatoire
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.
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## References

SHOWING 1-10 OF 19 REFERENCES
The distribution of the number of summands in the partitions of a positive integer
• Mathematics
• 1941
It is easily seen that the number of partitions of n having k or less summands is equal to the number of partitions of n in which no summand exceeds k . Thus the preceding results can be applied to
On hooks of Young diagrams
The well-known fact that there is always one more addable than removable box for a Young diagram is generalized to arbitrary hooks. As an application, this immediately implies a simple proof of a
Basic Hypergeometric Series
• Mathematics
• 1990
Foreword Preface 1. Basic hypergeometric series 2. Summation, transformation, and expansion formulas 3. Additional summation, transformation, and expansion formulas 4. Basic contour integrals 5.
Electronic letter to the authors, 18 sept
• 2001
On hooks of Young diagrams, Ann. of Comb
• On hooks of Young diagrams, Ann. of Comb
• 1998
Basic hypergeometric series, Cambridge University
• Press (Encycl. of Math. and its Appl.),
• 1990
Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux
• Acta Math . Sci . Hung .
• 1977
Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux , Soviet Math
• Acta Math . Sci . Hung .
• 1977
Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux, Soviet Math
• Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux, Soviet Math
• 1977