Some Properties of Abelian Return Words
M. Rigo, P. Salimov, and E. Vandomme
Department of Mathematics
University of Liège
Grande traverse 12 (B37)
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
nonzero 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.
Full version: pdf,
(Concerned with sequences
Received June 2 2012;
revised version received September 24 2012.
Published in Journal of Integer Sequences, March 2 2013.
Journal of Integer Sequences home page