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In introductory combinatorics, there is an emphasis on rook polynomials. But what is the significance of only considering rook polynomials? Why not consider "knight polynomials" or "bishop polynomials?"

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    There is? That's news to me.2011-08-01
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    "Despite the name's derivation from chess, the impetus for studying rook polynomials is their connection with counting permutations with restricted position" - from the Wikipedia article. I assume there is less connection with knight polynomials, so that the whole business with the chess pieces is just a way of visualizing a different problem.2011-08-01
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    And bishop polynomials **are** rook polynomials.2011-08-01
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    @Qiaochu: ‘Emphasis’ is too strong, but they are a pretty common topic in introductory books on combinatorics, ranging from Grimaldi (*Discrete and Combinatorial Mathematics*) and Tucker (*Applied Combinatorics*) at the lower end to Brualdi and (*Introductory Combinatorics*) and C.L. Liu (*Introduction to Combinatorial Mathematics*) at the higher end.2011-08-01

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