Mixable Shuffles, Quasi-shuffles and Hopf Algebras
  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. 
Kurusch Ebrahimi-Fard and Li Guo