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?"
Why study only rook polynomials?
7
$\begingroup$
combinatorics
soft-question
-
2There is? That's news to me. – 2011-08-01
-
7"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
-
0And bishop polynomials **are** rook polynomials. – 2011-08-01
-
0@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