Reference : Some properties of abelian return words
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/124311
Some properties of abelian return words
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 >]
2013
Journal of Integer Sequences
Univ. Waterloo Dept. Comput. Sci.
16
13.2.5
Yes (verified by ORBi)
International
1530-7638
Waterloo
Canada
[en] abelian ; return word ; sturmian word ; derived sequence ; combinatorics on words
[en] We investigate some properties of abelian return words as recently introduced by S. Puzynina and L. Q. 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/2268/124311
https://cs.uwaterloo.ca/journals/JIS/VOL16/Rigo/rigo3.html

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