Abstract

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.

Advisor

Moynihan, Matthew

Department

Mathematics

Disciplines

Discrete Mathematics and Combinatorics

Keywords

Combinatorics, Rook, Bishop, Rook polynomials, Latin Squares, Stirling numbers

Publication Date

2015

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis Exemplar

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© Copyright 2015 Stephen R. Skoch