Doubled Patterns are 3-Avoidable

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Doubled Patterns are 3-Avoidable

In combinatorics on words, a word w over an alphabet Σ is said to avoid a pattern p over an alphabet ∆ if there is no factor f of w such that f = h(p) where h : ∆∗ → Σ∗ is a non-erasing morphism. A pattern p is said to be k-avoidable if there exists an infinite word over a k-letter alphabet that avoids p. A pattern is said to be doubled if no variable occurs only once. Doubled patterns with at ...

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3-Abelian Cubes Are Avoidable on Binary Alphabets

A k-abelian cube is a word uvw, where u, v, w have the same factors of length at most k with the same multiplicities. Previously it has been known that k-abelian cubes are avoidable over a binary alphabet for k ≥ 5. Here it is proved that this holds for k ≥ 3.

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2016

ISSN: 1077-8926

DOI: 10.37236/5618