Abstract
We present two related results on the prefix tree of all binary cube-free words. First, we show that non-branching paths in this tree are short: such a path from a node of nth level has length \(O(\log n)\). Second, we prove that the lower density of the set of branching points along any infinite path is at least 23/78. Our results are based on a technical theorem describing the mutual location of “almost cubes” in a cube-free word.
E.A. Petrova—Supported by the grant 16-31-00212 of the Russian Foundation of Basic Research.
A.M. Shur—Supported by the grant 16-01-00795 of the Russian Foundation of Basic Research.
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Petrova, E.A., Shur, A.M. (2017). On the Tree of Binary Cube-Free Words. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_22
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