MathDBNonexistence of extremal square-free words over a four-letter alphabet
Nonexistence of extremal square-free words over a four-letter alphabet
An extremal square-free word is a square-free word such that inserting any letter in any position introduces a square. The nonexistence conjecture. There are no extremal square-free words over an alphabet of size . Extremal square-free words exist over a ternary alphabet for all sufficiently large lengths, while no examples are known over alphabets of size or greater; the conjecture concerns the four-letter case specifically.
Sources & referencesView supporting material
Primary source
Carla Groenland and Tom Johnston, “The lengths for which bicrucial square-free permutations exist”, arXiv:2109.00502 (2022).
Additional references
2 papers in this index state this conjecture (2020–2021). The statement above is taken from the most recent of them; the others are arXiv:2001.11763.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
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