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Tree representation for χ9= green.

Tree representation for χ9= green.

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Let be positive integers. By definition, is the least positive integer such that, for any -coloring of the interval , there exists a monochromatic solution to . For , the numbers are classical Schur numbers. In this paper, we study the numbers for . 1. Introduction Ramsey theory, an area that has seen a remarkable burst of research activity during...