Unavoidable patterns in words (strings)

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Joseph Malkevitch
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Joined: Tue Aug 28, 2007 2:52 pm
Location: Jamaica, New York

Unavoidable patterns in words (strings)

Postby Joseph Malkevitch » Fri Jan 12, 2018 3:24 pm

Dear Colleagues,

There is a surprisingly rich theory in discrete mathematics of the study of strings - patterns of symbols taken from some alphabet, perhaps 0 and 1 or perhaps x, y, and z. Thus one can do algebra on strings by defining, by way of an example, an operation on two strings by juxtaposing them. Thus xy composted with yzx is xyyzx. This string could be written with exponential notation, thus, zz as z^2.

Here is an account of some recent progress made on a problem in the combinatorics of words, which deals with strings and patterns in those strings:

https://gilkalai.wordpress.com/2018/01/ ... -in-words/

This article deals with words of a certain kind (Zimin words) and when they avoid string patterns of certain lengths.


Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451



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