Student Colloquium Talk by Professor Kenny Barrese, Bucknell University
Abstract: Rook theory is a branch of mathematics which considers how many ways you can put rooks on a board so that no two are attacking each other. Here a “rook” is the usual chess piece, but the “board” that we are placing on probably is not an eight by eight square. One way to consider the numbers you obtain is as coefficients of a polynomial, the rook polynomial. It is a key result in rook theory that, if you define the rook polynomial correctly, it always factors completely! In fact, we will see that this factorization arises not by algebraic manipulation, but by counting things in a clever way.