@article {IOPORT.05817553,
    author       = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
    title        = {Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions.},
    year         = {2010},
    journal      = {Discrete Mathematics},
    volume       = {310},
    number       = {24},
    issn         = {0012-365X},
    pages        = {3584-3606},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/j.disc.2010.09.008},
    abstract     = {Summary: We introduce analogs of the Hopf algebra of free quasi-symmetric functions with bases labeled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products $\Gamma\wr\frak S_n$ and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf algebras appear as natural analogs of McMahon's multisymmetric functions. As a consequence, we obtain an internal product on ordinary multi-symmetric functions. We extend these constructions to Hopf algebras of colored parking functions, colored non-crossing partitions and parking functions of type $B$.},
    identifier   = {05817553},
}