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

Publication Date

2015

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis Exemplar

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© Copyright 2015 Stephen R. Skoch