Abstract
Cassaigne conjectured in 1994 that any pattern with m distinct variables of length at least 3(2m − 1) is avoidable over a binary alphabet, and any pattern with m distinct variables of length at least 2m is avoidable over a ternary alphabet. Building upon the work of Rampersad and the power series techniques of Bell and Goh, we obtain both of these suggested strict bounds. Similar bounds are also obtained for pattern avoidance in partial words, sequences where some characters are unknown.
This material is based upon work supported by the National Science Foundation under Grant No. DMS–1060775. We thank the referees of preliminary versions of this paper for their very valuable comments and suggestions.
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Blanchet-Sadri, F., Woodhouse, B. (2013). Strict Bounds for Pattern Avoidance. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_11
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DOI: https://doi.org/10.1007/978-3-642-38771-5_11
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