On four color monochromatic sets with nondecreasing diameter |
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Authors: | David J Grynkiewicz |
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Institution: | Mathematics 253-37, Caltech, Pasadena, CA 91125, USA |
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Abstract: | Let m and r be positive integers. Define f(m,r) to be the least positive integer N such that for every coloring of the integers 1,…,N with r colors there exist monochromatic subsets B1 and B2 (not necessarily of the same color), each having m elements, such that (a) max(B1)-min(B1)max(B2)-min(B2), and (b) max(B1)B2). We improve previous upper bounds to determine that f(m,4)=12m-9. |
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Keywords: | Nondecreasing diameter Rado Ramsey |
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