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Some Thoughts on Rook Polynomials on Square Chessboards

In: Applications of Fibonacci Numbers

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  • Dan Fielder

Abstract

A rook polynomial is a polynomial whose x k coefficient is the number of ways k rooks can be placed on the squares of an arbitrarily shaped chessboard so that no rooks share the same rows or columns. The k rooks are called non-taking. Rook polynomials pattern combinatorial situations, especially those involving restricted permutations. The conventional square board used in the game, chess, is but one configuration.

Suggested Citation

  • Dan Fielder, 2004. "Some Thoughts on Rook Polynomials on Square Chessboards," Springer Books, in: Frederic T. Howard (ed.), Applications of Fibonacci Numbers, pages 101-108, Springer.
    • Handle: RePEc:spr:sprchp:978-0-306-48517-6_11
    DOI: 10.1007/978-0-306-48517-6_11
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