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Words avoiding abelian inclusions. (English) Zbl 1021.68069

Summary: We study a generalization of abelian squares which we call abelian inclusions: a word \(uv\) is said to be an \(f(l)\)-inclusion if the commutative image of \(v\) majorizes that of \(u\), and \(|v|\leq|u|+ f(|u|)\). We prove that \(cl\)-inclusions are unavoidable, but \(c\)-inclusions are avoidable for an arbitrary constant \(c\).

MSC:

68R15 Combinatorics on words
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