| Discrete Calculus Problem: Find the minimal value of (2008) | |||||||||||||||
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| Abstract: We prove that the minimum number (asymptotically) of monochromatic Schur triples that a 2-coloring of [1, n] can have is n2 22 + O(n). This revised version fills in a minor and subtle gap discovered by M. Primak. (The revision also corrects (at no extra cost) a discrepancy between the solution in the paper and the solution obtained by Maple. In the paper H 1/2 should be H0 and H1 should be H 1/2 for the solutions to agree.) Tianjin, June 29, 1996: In a fascinating invited talk at the SOCA 96 combinatorics conference organized by Bill Chen, Ron Graham proposed (see also [GRR], p. 390): Problem ($100): Find (asymptotically) the least number of monochromatic Schur triples {i, j, i+ j} that may occur in a 2-coloring of the integers 1, 2,..., n. By renaming the two colors 0 and 1, the above is equivalent to the following | |||||||||||||||
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