I read on page 4 [here][1] that the Kostka coefficients $K_{\lambda,\mu}$ are specializations of the Littlewood-Richardson coefficients $c^\tau_{\sigma,\lambda}$ by specializing $\sigma,\tau$ depending on $\mu$ in a simple manner (certain sums of parts of $\mu$).

I have two questions: Is there a similar specialization/translation for Kostka coefficients obtained from skew shapes, $K_{\lambda,\mu}^\nu$ where $\lambda/\nu$ is a skew shape?

Secondly: Is there a way to "go back", i.e.
can I express $c^\tau_{\sigma,\lambda}$ as some linear combination of some 
skew Kostka coefficients $K_{\lambda,\mu}^\nu$?


I would like to see if polynomiality of the map
$n \mapsto K_{n \lambda, nw}^{n \nu}$ implies polynomiality for a similar map with LW-coefficients.


  [1]: http://lipn.univ-paris13.fr/~toumazet/biblio/ARTICLES/NTB.pdf