[en] We identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form $p \tau(\varphi(z) \varphi^2(z) \cdots)$ where $p, z$ are finite words, $\varphi$ is a 6-uniform morphism, and $\tau$ is a coding. This description yields a recurrence for the $i$th letter, which we use to prove that the sequence of letters is 6-regular with rank 188. More generally, we prove $k$-regularity for a sequence satisfying a recurrence of the same type.
Disciplines :
Mathematics
Author, co-author :
Rowland, Eric; Hofstra University > Mathematics
Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Avoiding 5/4-powers on the alphabet of nonnegative integers
Publication date :
21 August 2020
Journal title :
Electronic Journal of Combinatorics
ISSN :
1097-1440
eISSN :
1077-8926
Publisher :
Electronic Journal of Combinatorics, United States - Georgia
Volume :
27
Issue :
3
Pages :
Paper #3.42, 39pp.
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
BAEF - Belgian American Educational Foundation [BE]
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