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(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].

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon
• Keywords: Combinatorial Formula, EJC 2007, EJC 2010, Free Quasi-symmetric Functions, Special Cases