Rado Numbers for Two Systems of Linear Equations

Author

Anthony Glackin, South Dakota State UniversityFollow

Document Type

Thesis - Open Access

Award Date

2024

Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Donald Vestal

Abstract

For any positive integer n and any equation E of either the form x1+x2+· · ·+xn = x0 or x1 + x2 + n = x0, the two-color Rado number R2(E) is the least integer such that any 2-coloring of the natural numbers 1 through R2(E) will contain a monochromatic solution to E. Let Ek be a system of k equations of the aforementioned form, where Ei represents the ith equation in Ek and the set I = {1, 2, . . . , k} is the set of indices of these equations. This thesis shows that the two-color Rado number R2(E) for the system of equations is R2(E) = R2(Em), where Em is the equation within E that has the largest Rado number.

Publisher

South Dakota State University

Recommended Citation

Glackin, Anthony, "Rado Numbers for Two Systems of Linear Equations" (2024). Electronic Theses and Dissertations. 990.
https://openprairie.sdstate.edu/etd2/990