Article (Scientific journals)
Critical exponents of infinite balanced words
Rampersad, Narad; Shallit, Jeffrey; Vandomme, Elise
2018In Theoretical Computer Science, In press
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Keywords :
Infinite word; Balanced word; Sturmian word; Critical exponent
Abstract :
[en] Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2+\sqr{2}/2 . Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5+\sqr{5})/4. Over larger alphabets, we give some candidates for balanced words (found computationally) having small critical exponents. We also explore a method for proving these results using the automated theorem prover Walnut.
Disciplines :
Mathematics
Author, co-author :
Rampersad, Narad;  University of Winnipeg
Shallit, Jeffrey;  University of Waterloo > School of Computer Science
Vandomme, Elise ;  Université de Liège - ULiège > Département de mathématique > Probabilités et statistique mathématique
Language :
English
Title :
Critical exponents of infinite balanced words
Publication date :
2018
Journal title :
Theoretical Computer Science
ISSN :
0304-3975
Publisher :
Elsevier, Netherlands
Volume :
In press
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 17 January 2019

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