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
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