Abelian returns in Sturmian words
  In this paper we study an abelian version of the notion of return word. Our main result is a new characterization of Sturmian words via abelian returns. Namely, we prove that a word is Sturmian if and only if each of its factors has two or three abelian returns. In addition, we describe the structure of abelian returns in Sturmian words, and discuss connections between abelian returns and periodicity. 
Svetlana Puzynina (University of Turku, Finland, and Sobolev Institute   of Mathematics, Novosibirsk, Russia), Luca Q. Zambo...
cs.FL cs.DM math.CO