A short proof of the rook reciprocity theorem
Summary: 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.
scientific article; zbMATH DE number 861598