Séminaire Lotharingien de Combinatoire, B61Aj (2010), 22 pp.
Nantel Bergeron and Philippe Choquette
We introduce hyperoctahedral species ($\H$-species) or species of type
which are analogous to the classical tensor species, but on which we
consider the action of the groups of signed permutations. We give
a bistrong monoidal functor, a functor which preserves Hopf
monoids, between the monoidal categories of species and
H-species. We also define bilax monoidal functors (functors
which preserve the structure of bimonoids) between the category of
H-species and the category of graded vector spaces. Using these
functors, the combinatorial Hopf algebra DQSym is shown to
arise from the cofree comonoid on the exponential species.
Received: December 10, 2008.
Revised: September 15, 2009; September 16, 2010.
Accepted: September 29, 2010.
The following versions are available: