Words Avoiding Abelian Inclusions
Sergei V. Avgustinovich, Anna E. Frid · 2002
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 $c$.