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Avoidability of Palindrome Patterns

Pascal Ochem 1 Matthieu Rosenfeld 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We characterize the formulas that are avoided by every $\alpha$-free word for some $\alpha>1$. We show that the avoidable formulas whose fragments are of the form $XY$ or $XYX$ are $4$-avoidable. The largest avoidability index of an avoidable palindrome pattern is known to be at least $4$ and at most $16$. We make progress toward the conjecture that every avoidable palindrome pattern is $4$-avoidable.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-03371500
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Submitted on : Friday, October 8, 2021 - 4:43:15 PM
Last modification on : Wednesday, October 13, 2021 - 3:35:38 AM

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Distributed under a Creative Commons Attribution - NoDerivatives 4.0 International License

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Pascal Ochem, Matthieu Rosenfeld. Avoidability of Palindrome Patterns. The Electronic Journal of Combinatorics, Open Journal Systems, 2021, 28 (1), pp.#1.4. ⟨10.37236/9593⟩. ⟨lirmm-03371500⟩

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