Geodesic
Dodgon's determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN
The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2
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I give a bijective proof of the Reverend Charles Lutwidge Dodgson's Rule: $$ \det \left [ (a_{i,j})_{ {1 \leq i \leq n } \atop {1 \leq j \leq n }} \right ] \cdot \det \left [ (a_{i,j})_{ {2 \leq i \leq n-1 } \atop {2 \leq j \leq n-1 }} \right ] \, = $$ $$ \det \left [ (a_{i,j})_{ {1 \leq i \leq n-1 } \atop {1 \leq j \leq n-1 }} \right ] \cdot \det \left [ (a_{i,j})_{ {2 \leq i \leq n } \atop {2 \leq j \leq n }} \right ] \,-\, \det \left [ (a_{i,j})_{ {1 \leq i \leq n-1 } \atop {2 \leq j \leq n }} \right ] \cdot \det \left [ (a_{i,j})_{ {2 \leq i \leq n } \atop {1 \leq j \leq n-1 }} \right ]\quad . $$
DOI : 10.37236/1337
Classification : 05A05, 15A15
Mots-clés : Dodgon's determinant-evaluation rule 
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     author = {Doron Zeilberger},
     title = {Dodgon's determinant-evaluation rule proved by {TWO-TIMING} {MEN} and {WOMEN}},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {2},
     doi = {10.37236/1337},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/1337/}
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Doron Zeilberger. Dodgon's determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN. The electronic journal of combinatorics, The Wilf Festschrift volume, Tome 4 (1997) no. 2. doi: 10.37236/1337

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