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.

Library of Congress Subject Headings

Ramsey theory.
Combinatorial analysis.
Rado numbers

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