Words Avoiding Abelian Inclusions

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