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A156989
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Largest size of a subset of {1,2,3}^n that does not contain any combinatorial lines (i.e., strings formed by 1, 2, 3, and at least one instance of a wildcard x, with x then substituted for 1, 2, or 3, e.g. 12x3x gives the combinatorial line 12131, 12232, 12333.)
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2
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OFFSET
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0,2
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COMMENTS
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The density Hales-Jewett theorem implies that a(n) = o(3^n). a(n) is studied further in the polymath1 project, see link below.
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LINKS
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EXAMPLE
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For n=2, one example that shows a(2) is at least 6 is { 11, 13, 22, 23, 31, 32 }.
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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STATUS
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approved
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