The number of binary rotation words

Anna E. Frid (1) , Damien Jamet (2)

1 I2M - Institut de Mathématiques de Marseille
2 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the precise asymptotics for it, which happens to be O(n^4). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov in 1982, then independently by Berenstein, Kanal, Lavine and Olson in 1987, Mignosi in 1991, and then with another technique by Berstel and Pocchiola in 1993.

Mots clés: total complexity; rotation; rotation words; Sturmian words; subword complexity

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Systèmes dynamiques [math.DS]

Anna E. Frid, Damien Jamet. The number of binary rotation words. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2014, 48 (4), pp.453 - 465. ⟨10.1051/ita/2014019⟩. ⟨hal-01089726⟩