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On ternary square-free circular words
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Arseny M. Shur
| Citations: | 1 - 1 self |
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@MISC{Shur_onternary,
author = {Arseny M. Shur},
title = {On ternary square-free circular words},
year = {}
}
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Abstract
Circular words are cyclically ordered finite sequences of letters. We give a computer-free proof of the following result by Currie: square-free circular words over the ternary alphabet exist for all lengths l except for 5, 7, 9, 10, 14, and 17. Our proof reveals an interesting connection between ternary square-free circular words and closed walks in the K3,3 graph. In addition, our proof implies an exponential lower bound on the number of such circular words of length l and allows one to list all lengths l for which such a circular word is unique up to isomorphism.
