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A direct bijective proof of the hook-length formula

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.
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https://hal.inria.fr/hal-00955690
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Jean-Christophe Novelli, Igor Pak, Alexander V. Stoyanovskii. A direct bijective proof of the hook-length formula. Discrete Mathematics and Theoretical Computer Science, DMTCS, 1997, Vol. 1, pp.53-67. ⟨10.46298/dmtcs.239⟩. ⟨hal-00955690⟩

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