Inversion of some series of free quasi-symmetric functions

Florent Hivert (1) , Jean-Christophe Novelli (2) , Jean-Yves Thibon (2)

1 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

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].

Domaines: Combinatoire [math.CO]

Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. Inversion of some series of free quasi-symmetric functions. 2008. ⟨hal-00325271⟩