Inversion of some series of free quasi-symmetric functions (Q1041180)

This paper gives a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form \({\mathbb F}_\omega(I)\) where \(I\) runs over compositions with parts in a prescribed set \(C\). This proves in particular three special cases (no restriction, even part, and all parts equal to 2) which were conjectured by B.C.V. Ung.