Talk:Unavoidable pattern

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 $A$=$B$=$y$. 81.132.13.71 (talk) 23:26, 29 November 2017 (UTC)