The number of binary rotation words
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 . We also give the precise asymptotics for it, which happens to be ( ). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov [39 (1982) 67–84], then independently by Mignosi [82 (1991) 71–84], and others.