A Characterization of Sturmian Words by Return Words

A Characterization of Sturmian Words by Return Words

1 R esum e: Nous pr esentons une nouvelle caract erisation des mots de Sturm bas ee sur les mots de retour. Si l'on consid ere chaque occurrence d'un mot w dans un mot innni r ecurrent, on d eenit l'ensemble des mots de retour de w comme l'ensemble de tous les mots distincts commenn cant par une occurrence de w et nissant exactement avant l'occurrence suivante de w. Le r esultat principal montr...

Return words in Sturmian and episturmian words

Considering each occurrence of a word w in a recurrent infinite word, we define the set of return words of w to be the set of all distinct words beginning with an occurrence of w and ending exactly just before the next occurrence of w in the infinite word. We give a simpler proof of the recent result (of the second author) that an infinite word is Sturmian if and only if each of its factors has...

A Characterization of Bispecial Sturmian Words

A finite Sturmian word w over the alphabet {a, b} is left special (resp. right special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial Sturmian word is a Sturmian word that is both left and right special. We show as a main result that bispecial Sturmian words are exactly the maximal internal factors of Christoffel words, that are words coding the digital approximations of s...

Sturmian Words: Dynamical Systems and Derivated Words

Sturmian Words, Lyndon Words and Trees

We prove some new combinatorial properties of the set PER of all words w having two periods p and q which are coprimes and such that w = p + q 2 [4,3]. We show that aPERb U {a, b} = St n Lynd, where St is the set of the finite factors of all infinite Sturmian words and Lynd is the set of the Lyndon words on the alphabet {a, b}. It is also shown that aPERb U {a, b} = CP, where CP is the set of C...