• 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}
}
  • R. Bacher, L. Manivel
  • 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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16 Citations
Highly Influential Citations
3
Background Citations
6
Methods Citations
2

16 Citations

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Citation Type

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TLDR
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The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the…
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Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms.…
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