Geodesic
Hyperoctahedral Species
Séminaire lotharingien de combinatoire, 61A (2009-2011)

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We introduce hyperoctahedral species ($\H$-species) or species of type B, 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. 

@article{SLC_2009-2011_61A_a9,
     author = {Nantel Bergeron and Philippe Choquette},
     title = {Hyperoctahedral {Species}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {61A},
     year = {2009-2011},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a9/}
}
TY  - JOUR
AU  - Nantel Bergeron
AU  - Philippe Choquette
TI  - Hyperoctahedral Species
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2011
VL  - 61A
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a9/
ID  - SLC_2009-2011_61A_a9
ER  - 
%0 Journal Article
%A Nantel Bergeron
%A Philippe Choquette
%T Hyperoctahedral Species
%J Séminaire lotharingien de combinatoire
%D 2009-2011
%V 61A
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a9/
%F SLC_2009-2011_61A_a9
Nantel Bergeron; Philippe Choquette. Hyperoctahedral Species. Séminaire lotharingien de combinatoire, 61A (2009-2011). http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a9/