Geodesic
A short proof of the rook reciprocity theorem
The electronic journal of combinatorics, Tome 3 (1996) no. 1
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Rook numbers of complementary boards are related by a reciprocity law. A complicated formula for this law has been known for about fifty years, but recently Gessel and the present author independently obtained a much more elegant formula, as a corollary of more general reciprocity theorems. Here, following a suggestion of Goldman, we provide a direct combinatorial proof of this new formula.
DOI : 10.37236/1234
Classification : 05A99
Mots-clés : complementary boards, reciprocity 
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     title = {A short proof of the rook reciprocity theorem},
     journal = {The electronic journal of combinatorics},
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     number = {1},
     doi = {10.37236/1234},
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Timothy Chow. A short proof of the rook reciprocity theorem. The electronic journal of combinatorics, Tome 3 (1996) no. 1. doi: 10.37236/1234

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