Minimal Hales-Jewett Sets
Existence And Structure
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A structure is Ramseyian if whenever it is divided into r classes, one of the classes exhibits properties similar to the whole structure. One of the concerns of Ramsey Theory is finding the smallest integer or set size for which a particular property holds. The Hales-Jewett Theorem is one of the major results of Ramsey Theory. In this work, the existence of minimal Hales-Jewett sets is established, and one is specifically identified.
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