Binary shuffle bases for quasi-symmetric functions
Combinatorics
2013-05-23 v1
Abstract
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 Jour. 25 (2011) 307-317] 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].
Cite
@article{arxiv.1305.5032,
title = {Binary shuffle bases for quasi-symmetric functions},
author = {Jean-Christophe Novelli and Jean-Yves Thibon},
journal= {arXiv preprint arXiv:1305.5032},
year = {2013}
}
Comments
17 pages