The analogs of overlap-freeness for the period-doubling morphism and for the Fibonacci morphism

James Currie
The University of Winnipeg, Manitoba, Canada

Date(s) : 26/09/2023   iCal
15 h 00 min - 16 h 00 min

The Thue-Morse morphism is the binary map . A word is overlap-free if it has no factor of the form , where is non-empty. A deep connection between these two concepts is the engine behind several results:

– The precise characterization of finite prefixes of infinite overlap-free binary words (Fife’s Theorem);

– A precise enumeration of overlap-free binary words;

– A characterization of all binary patterns encountered by the Thue-Morse word;

– The determination of the lexicographically least infinite overlap-free word.

Given another morphism, is there an analog of overlap-freeness which facilitates the proof of similar results? We show that the answer is yes for the period doubling morphism , and for the Fibonacci morphism .


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