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Some properties of abelian return words (long abstract)
Rigo, Michel; Salimov, Pavel; Vandomme, Elise
2012Journées montoises d'informatique théorique
 

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Keywords :
return word; sturmian sequence; combinatorics on words
Abstract :
[en] We investigate some properties of abelian return words as recently introduced by Puzynina and Zamboni. In particular, we obtain a characterization of Sturmian words with non-null intercept in terms of the finiteness of the set of abelian return words to all prefixes. We describe this set of abelian returns for the Fibonacci word but also for the 2-automatic Thue–Morse word. We also investigate the relationship existing between abelian complexity and finiteness of the set of abelian returns to all prefixes. We end this paper by considering the notion of abelian derived sequence. It turns out that, for the Thue–Morse word, the set of abelian derived sequences is infinite.
Disciplines :
Mathematics
Author, co-author :
Rigo, Michel  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Salimov, Pavel ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Vandomme, Elise ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Some properties of abelian return words (long abstract)
Publication date :
11 September 2012
Event name :
Journées montoises d'informatique théorique
Event organizer :
R. Jungers
Event date :
from 11-9-2012 to 14-9-2012
Audience :
International
Available on ORBi :
since 19 September 2012

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