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Abstract for Timothy Chow, A Short Proof of the Rook Reciprocity Theorem

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.

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