Date

4-26-2024

Document Type

Thesis

Abstract

One of the main goals in the study of Ramsey Theory is to find “order” in seemingly “random” structures. For example, Van der Waerden’s Theorem tells us that given any r-coloring of the positive integers, there will exist arbitrarily long monochromatic arithmetic progressions. The theorem places no requirement on the gap (common difference), d, of the arithmetic progression – it can be any natural number. With this in mind, we ask if we are still guaranteed arbitrarily long monochromatic arithmetic progressions when we restrict the possible values of d to some subset D ⊆ N. We also ask a similar question: are we guaranteed arbitrarily long monochromatic sequences x1 < x2 < · · · < xk where xi − xi−1 ∈ D?

Department

Mathematics

Thesis Comittee

Dr. Jacqueline Anderson, Thesis Advisor
Dr. Ward Heilman, Committee Member
Dr. John Pike, Committee Member

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