Article (Scientific journals)
On a group theoretic generalization of the Morse-Hedlund theorem
Charlier, Emilie; Puzynina, Svetlana; Zamboni, Luca
2017In Proceedings of the American Mathematical Society, 145 (8), p. 3381–3394
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Keywords :
combinatorics on words; aperiodicty; Morse-Hedlund theorem
Abstract :
[en] In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund proved that every aperiodic infinite word contains at least n+ 1 distinct factors of each length n. They further showed that an infinite word has exactly n+ 1 distinct factors of each length n if and only if it is binary, aperiodic and balanced, i.e., it is a Sturmian word. In this paper we obtain a broad generalization of the Morse-Hedlund theorem via group actions.
Disciplines :
Mathematics
Author, co-author :
Charlier, Emilie  ;  Université de Liège > Département de mathématique > Mathématiques discrètes
Puzynina, Svetlana
Zamboni, Luca
Language :
English
Title :
On a group theoretic generalization of the Morse-Hedlund theorem
Publication date :
2017
Journal title :
Proceedings of the American Mathematical Society
ISSN :
0002-9939
eISSN :
1088-6826
Publisher :
American Mathematical Society
Volume :
145
Issue :
8
Pages :
3381–3394
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 28 January 2016

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