Inversion of some series of free quasi-symmetric functions
  We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form F_{\omega(I)} where I runs over compositions with parts in a prescribed set C. This proves in particular three special cases (no restriction, even parts, and all parts equal to 2) which were conjectured by B. C. V. Ung in [Proc. FPSAC'98, Toronto]. 
Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon