Reference : Some properties of abelian return words (long abstract)
Scientific congresses and symposiums : Unpublished conference
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/130665
Some properties of abelian return words (long abstract)
English
Rigo, Michel mailto [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
Salimov, Pavel [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
Vandomme, Elise mailto [Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]
11-Sep-2012
Yes
No
International
Journées montoises d'informatique théorique
from 11-9-2012 to 14-9-2012
R. Jungers
Louvain-La-Neuve
[en] return word ; sturmian sequence ; combinatorics on words
[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.
Researchers
http://hdl.handle.net/2268/130665

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