BINARY WORDS AVOIDING THE PATTERN AABBCABBA
We show that there are three types of infinite words over the two-letter alphabet {0, 1} that avoid the pattern AABBCABBA. These types, P, E(0), and E(1), differ by the factor complexity and the asymptotic frequency of the letter 0. Type P has polynomial factor complexity and letter frequency 1/2. Type E(0) has exponential factor complexity and the frequency of the letter 0 is at least 0.45622 and at most 0.48684. Type E(1) is obtained from type E(0) by exchanging 0 and 1.
factor complexity letter frequency combinatorics on words