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
Bachelor of Arts
Senior Independent Study Thesis Exemplar
© Copyright 2015 Stephen R. Skoch