Inversion of some series of free quasi-symmetric functions |
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| Authors: | Florent Hivert Jean-Christophe Novelli Jean-Yves Thibon |
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| Affiliation: | aLITIS, Université de Rouen, Avenue de l’université, 76801 Saint Étienne du Rouvray, France;bUniversité Paris-Est, Institut Gaspard Monge, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France |
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| Abstract: | We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form  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 [B.C.V. Ung, Combinatorial identities for series of quasi-symmetric functions, in: Proc. FPSAC’08, Toronto, 2008]. |
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