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Journal Articles The Electronic Journal of Combinatorics Year : 2021

Avoidability of Palindrome Patterns

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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lirmm-03371500 , version 1 (08-10-2021)

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