Permutation pattern matching in strings Loosely speaking, permutation pattern matching deals with problems of the following kind: 


  Given permutations $\pi$ in $S_n$ and $\sigma$ in $S_m$, with $m\leq n$, does $\pi$ contain a subsequence $\tau$ of length $m$ whose elements are ordered according to $\sigma$?


For example, if $\pi=\langle 3\ 1\ 5\ 4\ 2\ 8\ 6\ 7\rangle$ and $\sigma=\langle 2\ 1\ 3\rangle$, then the subsequence $3\ 1\ 4$ matches $\sigma$. As you can see, we're not looking here for an exact match, but rather for something that "looks like" the specified pattern.

Does anyone know whether work has been conducted on extending permutation pattern matching problems to strings? Google unfortunately did not help, since the well-known pattern matching problem on strings has nothing to do with this.
I finally managed to dig out a nice survey by Kitaev and Mansour, which gives pointers to the literature related to permutation pattern matching on  "usual"/signed/coloured permutations and words.