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Rook theory. I. Rook equivalence of Ferrers boards
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We introduce a new tool, the factorial polynomials, to study rook equivalence of Ferrers boards. We provide a set of invariants for rook equivalence as well as a very simple algorithm for deciding rook equivalence of Ferrers boards. We then count the number of Ferrers boards rook equivalent to a given Ferrers board.
American Mathematical Society (AMS)
Title: Rook theory. I. Rook equivalence of Ferrers boards
Description:
We introduce a new tool, the factorial polynomials, to study rook equivalence of Ferrers boards.
We provide a set of invariants for rook equivalence as well as a very simple algorithm for deciding rook equivalence of Ferrers boards.
We then count the number of Ferrers boards rook equivalent to a given Ferrers board.
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