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The number of ternary words avoiding abelian cubes grows exponentially. (English) Zbl 1101.68741

Summary: We show that the number of ternary words of length \(n\) avoiding abelian cubes grows faster than \(r^n\), where \(r = 2^{1/24}\).

MSC:

68R15 Combinatorics on words
05A05 Permutations, words, matrices

Software:

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Online Encyclopedia of Integer Sequences:

Number of Abelian cubefree words over a 3-letter alphabet.