## 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

### Keywords:

abelian inclusions