Pattern avoidance in partial words over a ternary alphabet

Adam Gągol

Abstract


Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with \(m\) distinct variables and of length at least \(2^m\) is avoidable over a ternary alphabet and if the length is at least \(3\cdot 2^{m-1}\) it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.

Keywords


Formal languages; combinatorics on words; pattern avoidance; partial words; entropy compression; probabilistic method

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References


Blanchet-Sadri, F., Woodhouse, B., Strict Bounds for Pattern Avoidance, Theoret. Comput. Sci. 506 (2013), 17–28.

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DOI: http://dx.doi.org/10.17951/a.2015.69.1.73
Date of publication: 2015-11-30 09:21:11
Date of submission: 2015-09-03 12:33:44


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