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)[reply]

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)[reply]