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A bijective proof of the Jacobi identity and reconstruction of Young diagrams

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Abstract

A short combinatorial proof is given of the classical Jacobi identity from the theory of theta-functions.

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Literature cited

  1. M. Hall, Combinatorics [Russian translation], Moscow (1970).

  2. Z. M. Leibenzon, “A simple combinatorial method for proving the Jacobi identity and its generalizations,” Funkts. Anal. Prilozhen.,20, No. 1, 77–78 (1986).

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  3. G. Andrews, Theory of Partitions [Russian translation], Moscow (1982).

  4. D. B. Fuks, Cohomology of Infinite-Dimensional Lie Algebras [in Russian], Moscow (1984).

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Authors
  1. A. M. Vershik
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 3–6, 1986.

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Vershik, A.M. A bijective proof of the Jacobi identity and reconstruction of Young diagrams. J Math Sci 41, 889–891 (1988). https://doi.org/10.1007/BF01247084

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  • DOI: https://doi.org/10.1007/BF01247084

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