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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 deenitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. We nish with some examples.
1. The main result of the article is a bijective proof of the multiplicative formula for the dimension of an irreducible representation of the symmetric group, which is usually called the "hook-length formula." We also prove a formula for the Poincar6 series for the multiplicity of the isotypic component in the symmetric algebra S (V) (V = C ~) considered… (More)