A Bijective Proof of Borchardt's Identity

descriptionPublicationkeyboard_double_arrow_right Article 26 Jul 2004Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 11 (eissn: 1077-8926,

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Authors: Dan Singer;

doi: 10.37236/1801

A Bijective Proof of Borchardt's Identity

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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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Minnesota State University, Mankato
United States

Keywords

sign-reversing involution, alternating sign matrix, determinant, permanent, Combinatorial identities, bijective combinatorics, Borchardt's identity

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