There are level ternary circular square-free words of length $n$ for $n\ne 5,7,9,10,14,17.$

Abstract

A word is level if each letter appears in it the same number of times, plus or minus 1. We give a complete characterization of the lengths for which level ternary circular square-free words exist.

Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101

“…Theorem 3. [4,8] There is a level ternary circular square-free word of length n, exactly when n is a positive integer, n = 5, 7, 9, 10, 14, 17.…”

“…To produce circular FS words with specific lengths, we make use of the following recent result by the authors [4,8]:…”