Geodesic
Mixable shuffles, quasi-shuffles and Hopf algebras.
Journal of Algebraic Combinatorics, Tome 24 (2006) no. 1, pp. 83-101.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras. 
@article{JAC_2006__24_1_a1,
     author = {Ebrahimi-Fard, Kurusch and Guo, Li},
     title = {Mixable shuffles, quasi-shuffles and {Hopf} algebras.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {83--101},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2006__24_1_a1/}
}
TY  - JOUR
AU  - Ebrahimi-Fard, Kurusch
AU  - Guo, Li
TI  - Mixable shuffles, quasi-shuffles and Hopf algebras.
JO  - Journal of Algebraic Combinatorics
PY  - 2006
SP  - 83
EP  - 101
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2006__24_1_a1/
LA  - en
ID  - JAC_2006__24_1_a1
ER  - 
%0 Journal Article
%A Ebrahimi-Fard, Kurusch
%A Guo, Li
%T Mixable shuffles, quasi-shuffles and Hopf algebras.
%J Journal of Algebraic Combinatorics
%D 2006
%P 83-101
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2006__24_1_a1/
%G en
%F JAC_2006__24_1_a1
Ebrahimi-Fard, Kurusch; Guo, Li. Mixable shuffles, quasi-shuffles and Hopf algebras.. Journal of Algebraic Combinatorics, Tome 24 (2006) no. 1, pp. 83-101. http://geodesic.mathdoc.fr/item/JAC_2006__24_1_a1/