Talk:Unavoidable pattern

The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

It is requested that an image or photograph of Unavoidable pattern be included in this article to improve its quality. Please replace this template with a more specific media request template where possible.
The Free Image Search Tool or Openverse Creative Commons Search may be able to locate suitable images on Flickr and other web sites.

Upload

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]