Rook theory is the study of permutations described using terminology from the game of chess. In rook theory, a generalized board B is any subset of the squares of an n x n square chessboard for some positive integer n. Rook numbers count the number of ways to place non-attacking rooks on a generalized board, and the rook polynomial is a polynomial that organizes the rook numbers for a board B. In our research, we classified all quadratic polynomials that are the rook polynomial for some generalized board B.
Professor Frederick Butler, Department of Physical Sciences, York College of Pennsylvania
"A Classification of Quadratic Rook Polynomials,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 15
, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss1/4