Geodesic
Avoidability of palindrome patterns
The electronic journal of combinatorics, Tome 28 (2021) no. 1
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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.
DOI : 10.37236/9593
Classification : 68R15
Mots-clés : infinite word, palindrome, avoidability 
@article{10_37236_9593,
     author = {Pascal Ochem and Matthieu Rosenfeld},
     title = {Avoidability of palindrome patterns},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {1},
     doi = {10.37236/9593},
     zbl = {1477.68254},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9593/}
}
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Pascal Ochem; Matthieu Rosenfeld. Avoidability of palindrome patterns. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9593

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