The Ramanujan Journal

, Volume 40, Issue 1, pp 207–225 | Cite as

Binary shuffle bases for quasi-symmetric functions

  • Jean-Christophe Novelli
  • Jean-Yves Thibon


We construct bases of quasi-symmetric functions whose product rule is given by the shuffle of binary words, as for multiple zeta values in their integral representations, and then extend the construction to the algebra of free quasi-symmetric functions colored by positive integers. As a consequence, we show that the fractions introduced in Guo and Xie (Ramanujan J 25:307–317, 2011) provide a realization of this algebra by rational moulds extending that of free quasi-symmetric functions given in Chapoton et al. (Int Math Res Not IMRN 2008, no. 9, Art. ID rnn018, 2008).


Noncommutative symmetric functions Quasi-symmetric functions Shuffle Multiple Zeta Values 

Mathematics Subject Classification

05E05 16T30 11M32 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Laboratoire d’Informatique Gaspard MongeUniversité Paris-Est Marne-la-ValléeMarne-la-Vallée Cedex 2France

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