Key Words: Well quasi orders, Combinatorics on words
Given a set $I$ of words, the set $L^\epsilon _{\vdash _I}$ of all
words obtained by the shuffle of (copies of) words of $I$ is
naturally provided with a partial order: for $u, v$ in
$L^\epsilon _{\vdash _I}$, $u \vdash^*_I v$ if and only if $v$ is
the shuffle of $u$ and another word of $L^\epsilon _{\vdash _I}$. In a previous paper, the authors have opened
the problem of the characterization of the finite sets $I$ such
that $\vdash_I^*$ is a well quasi-order on
$L^\epsilon _{\vdash _I}$. In this paper we give the answer in the
case when $I$ consists of a single word $w$.
