This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.
Skoch, Stephen R., "I Don't Play Chess: A Study of Chess Piece Generating Polynomials" (2015). Senior Independent Study Theses. Paper 6559.
Discrete Mathematics and Combinatorics
Combinatorics, Rook, Bishop, Rook polynomials, Latin Squares, Stirling numbers
Bachelor of Arts
Senior Independent Study Thesis Exemplar
© Copyright 2015 Stephen R. Skoch