Factor Colorings of Linearly Recurrent Words
Ville Salo, Ilkka T\"orm\"a
TL;DR
This paper investigates how to color factors of aperiodic linearly recurrent infinite words to prevent monochromatic factorizations, revealing the existence of such colorings.
Contribution
It demonstrates that for these words, there always exists a coloring avoiding monochromatic factorizations into increasing length factors.
Findings
Existence of colorings avoiding monochromatic factorizations
Applicable to aperiodic linearly recurrent infinite words
Advances understanding of combinatorial properties of infinite words
Abstract
In this short article, we study factor colorings of aperiodic linearly recurrent infinite words. We show that there always exists a coloring which does not admit a monochromatic factorization of the word into factors of increasing lengths.
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Taxonomy
Topicssemigroups and automata theory · Cellular Automata and Applications · DNA and Biological Computing