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Lagrange's identity and the hook formula

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Abstract

A simple combinatorial derivation of the hook formula for the dimensions of irreducible representations of the symmetric group is given

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Literature cited

  1. A. M. Vershik, “Hook formula and identities related to it,” Zapiski Nauchn. Semin. Leningr. Otdel. Mat. Inst.,172, 3–20 (1989).

    Google Scholar 

  2. I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Moscow (1985).

  3. G. James, Theory of Representations of Symmetric Groups [Russian translation], Moscow (1982).

  4. D. Knuth, The Art of Computer Programming [Russian translation], Vol. 3, Moscow (1978).

  5. A. N. Kirillov and N. Yu. Reshetikhin, “The Bethe Ansatz and combinatorics of Young tableaux,” Zap. Nauchn. Semin. Leningr. Otdel. Mat. Inst.,155, 65–115 (1986).

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  6. J. Frame, G. Robinson, and R. Thrall, “The hook graphs of Sn,” Can. J. Math.,6, 316–324 (1954).

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  7. D. S. Franzblau and D. Zeilberger, “A bijective proof of the hook-length formula,” J. Algorithms,3, 317–343 (1982).

    Google Scholar 

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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 78–87, 1989.

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Kirillov, A.N. Lagrange's identity and the hook formula. J Math Sci 59, 1078–1084 (1992). https://doi.org/10.1007/BF01480689

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  • DOI: https://doi.org/10.1007/BF01480689

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