Geodesic
A bijective proof of Borchardt's identity
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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We prove Borchardt's identity $$\hbox{det}\left({1\over x_i-y_j}\right) \hbox{per}\left({1\over x_i-y_j}\right)= \hbox{det}\left({1\over(x_i-y_j)^2}\right)$$ by means of sign-reversing involutions.
DOI : 10.37236/1801
Classification : 05A19
Mots-clés : Borchardt's identity, determinant, permanent, sign-reversing involution, alternating sign matrix 
@article{10_37236_1801,
     author = {Dan Singer},
     title = {A bijective proof of {Borchardt's} identity},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {1},
     doi = {10.37236/1801},
     zbl = {1053.05010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1801/}
}
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Dan Singer. A bijective proof of Borchardt's identity. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1801

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