Well Quasi Orders and the Shuffle Closure of Finite Sets.

Given a set I of words, the set L⊢Iε 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⊢Iε, u ⊢*Iv if and only if v is the shuffle of u and another word of L⊢Iε. In [3], the authors have stated the problem of the characterization of the finite sets I such that ⊢I* is a well quasi-order on L⊢Iε. In this paper we give the answer in the case when I consists of a single word w. [ABSTRACT FROM AUTHOR]