Talk:Unavoidable pattern

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Something's missing

Something must be missing, either in the definition of an unavoidable pattern or in the statement of the first example using Zimin words. Given two unique symbols, a and b, I can create an arbitrarily long strong that doesn't contain aba: ab, aaa, aaab, abbbb, aaabbb, bbaaaaa, etc., which refutes the claim that, in the example as stated, the pattern aba is unavoidable. Unless I'm missing something. Largoplazo ( talk) 17:07, 6 October 2017 (UTC)

This confused me for a moment too, but then I realized A and B in the pattern can relate to the same symbol in the string. If we make our unique symbols x and y instead, it's a bit clearer. 4 characters can avoid the pattern: e.g. xxyy. However 5 or more will match it, as they must contain either xyx, yxy, xxx, or yyy: e.g. xxyyy fits the pattern ABA where A=B=y. ( talk) 23:26, 29 November 2017 (UTC)