Document Type
Thesis - University Access Only
Award Date
2012
Degree Name
Master of Science (MS)
Department / School
Mathematics and Statistics
First Advisor
Daniel Schaal
Abstract
Given a linear equation, inequality, or system of equations/inequalities L, the t-color Rado number is the least integer n such that for every t-coloring of the ordered set (1, 2, ... , n) there is a monochromatic solution to L. If there is not such an integer, we will say the t-color Rado number is infinite. Bialostocki and Schaal determined the 2-color Rado numbers for the system x1 + x2 + · · · + Xm-1 < Xm where x1 < x2 < · · · < Xm, m 2:'.: 3. In this paper, we will add an integer constant to the first inequality in this system. In other words, we will find the 2-color Rado numbers for the system X1 + X2 + · · · + Xm-1 + c < Xm where X1 < X2 < · · · < Xm and m 2:'.: 3.
Library of Congress Subject Headings
Ramsey theory
Combinatorial analysis
Rado numbers
Publisher
South Dakota State University
Recommended Citation
Vorland, Corey, "Rado Numbers for some Non-Homogenous Inequalities" (2012). Electronic Theses and Dissertations. 1986.
https://openprairie.sdstate.edu/etd2/1986
Rights Statement
