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  1. Home > Articles & Issues >
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  3. A direct bijective p ...
Article

A direct bijective proof of the hook-length formula

Jean-Christophe Novelli (1), Igor Pak (2), Alexander V. Stoyanovskii (3)
(1) Laboratoire d'informatique Algorithmique : Fondements et Applications
(2) Department of Mathematics [Cambridge]
(3) Department of Mathematics [Moscou]
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Imported on
March 26, 2015
Published on
January 1, 1997
Last modified on
March 31, 2025
Volume 1
vol. 1
DOI
10.46298/dmtcs.239
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A direct bijective proof of the hook-length formula

Jean-Christophe Novelli (1), Igor Pak (2), Alexander V. Stoyanovskii (3)
(1) Laboratoire d'informatique Algorithmique : Fondements et Applications
(2) Department of Mathematics [Cambridge]
(3) Department of Mathematics [Moscou]
Abstract
This paper presents a new proof of the hook-length formula, which computes the number of standard Young tableaux of a given shape. After recalling the basic definitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. The paper concludes with some examples.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Hook-length formula
  • bijective proof
  • inverse algorithms
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