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Document Type

Thesis - University Access Only

Award Date

2013

Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Daniel Schaal

Abstract

Given a linear equation, the least integer n, provided it exists, such that for every t-coloring of the natural numbers {1, 2, . . . , n} there exists a monochromatic solution to the equation is called the t-color Rado number for the equation. In this paper, the 2-color Rado number for each of the following two equations is established:
2x1 + 2x2 + c = x3
and
2x1 + 2x2 + 2x3 + c = x4
where c is an integer. Given a linear equation, the least real number b, provided it exists, such that for every t-coloring of the interval [1, b] there exists a monochromatic solution to the equation is called the t-color continuous Rado number for the equation. In this paper, the 2-color continuous Rado number for the following family of equations is also established: a1x1 + a2x2 + · · · + am-1 xm-1 + c = xm

where m is an integer such that m ≥ 3, a1, a2, . . . , am-1 are natural numbers, and c is a real number.

Library of Congress Subject Headings

Ramsey theory
Combinatorial analysis

Description

Includes bibliographical references (pages 59-60).

Format

application/pdf

Number of Pages

65

Publisher

South Dakota State University

Rights

In Copyright - Non-Commercial Use Permitted
http://rightsstatements.org/vocab/InC-NC/1.0/

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