A Bijective Proof of Borchardt's Identity

Dan Singer

Abstract


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.


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