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.

Author Bio

Alicia Velek is a 2013 graduate of York College of Pennsylvania with a B.S. in Mathematics and minor in International Relations. This work was completed over the course of two semesters at York College. She currently works in the nonprofit sector but plans to enroll in graduate studies in Applied Mathematics in the near future. In her free time, she is an avid traveler and enjoys the beach.