Some 2-Color Rado Numbers For A Linear Equation With A Negative Constant

Author

Rachel Bergjord, South Dakota State UniversityFollow

Document Type

Thesis - Open Access

Award Date

2023

Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Daniel Schaal

Abstract

An r-coloring is a function Δ that assigns a color to each natural number from 1 to some number n using colors 0, 1, . . . , r − 1. A monochromatic solution (in Δ) to an equation L with m variables is an ordered m-tuple (x1, x2, . . . , xm) where Δ(x1) = Δ(x2) = · · · = Δ(xm) and (x1, x2, . . . , xm−1, xm) solves L. Given a linear equation L and t ∈ N, the t-color Rado number for L is the least integer n (if it exists) such that every Δ : [1, n] → [0, t − 1] admits a monochromatic solution to L. If no such integer exists, the t-color Rado number for L is infinite. We prove the following two theorems.

Library of Congress Subject Headings

Combinatorial analysis.
Ramsey theory.
Rado numbers.

Publisher

South Dakota State University

Recommended Citation

Bergjord, Rachel, "Some 2-Color Rado Numbers For A Linear Equation With A Negative Constant" (2023). Electronic Theses and Dissertations. 603.
https://openprairie.sdstate.edu/etd2/603