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Doubled Patterns with Reversal Are 3-Avoidable

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Combinatorics on Words (WORDS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12847))

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Abstract

In combinatorics on words, a word w over an alphabet \(\varSigma \) is said to avoid a pattern p over an alphabet \(\varDelta \) if there is no factor f of w such that \(f=h(p)\) where \(h:\varDelta ^*\rightarrow \varSigma ^*\) is a non-erasing morphism. A pattern p is said to be k-avoidable if there exists an infinite word over a k-letter alphabet that avoids p. A pattern is doubled if every variable occurs at least twice. Doubled patterns are known to be 3-avoidable. Currie, Mol, and Rampersad have considered a generalized notion which allows variable occurrences to be reversed. That is, \(h(V^R)\) is the mirror image of h(V) for every \(V\in \varDelta \). We show that doubled patterns with reversal are 3-avoidable.

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Correspondence to Pascal Ochem .

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Ochem, P. (2021). Doubled Patterns with Reversal Are 3-Avoidable. In: Lecroq, T., Puzynina, S. (eds) Combinatorics on Words. WORDS 2021. Lecture Notes in Computer Science(), vol 12847. Springer, Cham. https://doi.org/10.1007/978-3-030-85088-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-85088-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85087-6

  • Online ISBN: 978-3-030-85088-3

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