On a group theoretic generalization of the Morse-Hedlund theorem

Charlier, Emilie; Puzynina, Svetlana; Zamboni, Luca

doi:10.1090/proc/13589

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On a group theoretic generalization of the Morse-Hedlund theorem

Charlier, Emilie; Puzynina, Svetlana; Zamboni, Luca

2017 • In Proceedings of the American Mathematical Society, 145 (8), p. 3381–3394

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https://hdl.handle.net/2268/192556

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10.1090/proc/13589

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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 :

Pages :

3381–3394

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 28 January 2016

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