There are level ternary circular square-free words of length $n$ for $n\ne 5,7,9,10,14,17.$
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. Key words: combinatorics on words, circular words, necklaces, square-free words, non-repetitive sequences
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