Dodgson's Determinant-Evaluation Rule Proved by Two-Timing Men and Women

  • Doron Zeilberger

Abstract

I give a bijective proof of the Reverend Charles Lutwidge Dodgson's Rule: $$ \det \left [ (a_{i,j})_{ {1 \leq i \leq n } \atop {1 \leq j \leq n }} \right ] \cdot \det \left [ (a_{i,j})_{ {2 \leq i \leq n-1 } \atop {2 \leq j \leq n-1 }} \right ] \, = $$ $$ \det \left [ (a_{i,j})_{ {1 \leq i \leq n-1 } \atop {1 \leq j \leq n-1 }} \right ] \cdot \det \left [ (a_{i,j})_{ {2 \leq i \leq n } \atop {2 \leq j \leq n }} \right ] \,-\, \det \left [ (a_{i,j})_{ {1 \leq i \leq n-1 } \atop {2 \leq j \leq n }} \right ] \cdot \det \left [ (a_{i,j})_{ {2 \leq i \leq n } \atop {1 \leq j \leq n-1 }} \right ]\quad . $$

Published
1996-05-15