Rauzy's conjecture on ternary words of constant abelian complexity

An infinite word over a ternary alphabet has abelian complexity equal to the number of distinct Parikh vectors of its factors of each given length. Its letter-frequency vector records the limiting frequencies of the three letters, when these frequencies exist.

Rauzy's conjecture. Except for very particular vectors of letter frequencies, there do not exist any infinite ternary words with constant abelian complexity equal to $3$.

The conjecture concerns the classification of ternary words whose abelian complexity is minimal and constant. The source states that it admits trivial counterexamples, so the conjecture is refuted as written.