Geodesic
A bijective proof of the Jacobi identity and reshapings of the Young diagrams
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VIII, Tome 155 (1986), pp. 3-6

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An elementary combinatorial proof of the classical Jacobi identity for theta-series is presented. 
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     author = {A. M. Vershik},
     title = {A bijective proof of the {Jacobi} identity and reshapings of the {Young} diagrams},
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     publisher = {mathdoc},
     volume = {155},
     year = {1986},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_155_a0/}
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A. M. Vershik. A bijective proof of the Jacobi identity and reshapings of the Young diagrams. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part VIII, Tome 155 (1986), pp. 3-6. http://geodesic.mathdoc.fr/item/ZNSL_1986_155_a0/