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Faculty Mentor

Daniel Schaal

Abstract

This paper will examine the type of Ramsey theory concerned with the preservation of solution to specific linear equations under set partition. That is, if a solution to a linear equation exists in the natural numbers, must one also exist within one set of a partition of the natural numbers? To differentiate sets of a partition of the natural numbers from one another, it is convenient to use colors. Then a solution in just one set of a partition of the natural numbers can be referred to as monochromatic solution, or a solution in a single color. [Page 1]

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Mathematics Commons

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