A short proof of the rook reciprocity theorem (Q1909977)
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scientific article; zbMATH DE number 861598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short proof of the rook reciprocity theorem |
scientific article; zbMATH DE number 861598 |
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A short proof of the rook reciprocity theorem (English)
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21 July 1996
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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.
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complementary boards
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reciprocity
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