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 most 3 variables and patterns with at least 6 variables are 3-avoidable. We show that doubled patterns with 4 and 5 variables are also 3-avoidable.

• Type: Journal
• Year: 2016
• Where: COMBINATORICS
• Authors: Pascal Ochem
• Keywords: COMBINATORICS 2016