Geodesic
Binomial Species and Combinatorial Exponentiation
Séminaire lotharingien de combinatoire, Tome 78 (2018-2020) 
Gilbert Labelle. Binomial Species and Combinatorial Exponentiation. Séminaire lotharingien de combinatoire, Tome 78 (2018-2020). http://geodesic.mathdoc.fr/item/SLC_2018-2020_78_a0/
@article{SLC_2018-2020_78_a0,
     author = {Gilbert Labelle},
     title = {Binomial {Species} and {Combinatorial} {Exponentiation}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018-2020},
     volume = {78},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018-2020_78_a0/}
}
TY  - JOUR
AU  - Gilbert Labelle
TI  - Binomial Species and Combinatorial Exponentiation
JO  - Séminaire lotharingien de combinatoire
PY  - 2018-2020
VL  - 78
UR  - http://geodesic.mathdoc.fr/item/SLC_2018-2020_78_a0/
ID  - SLC_2018-2020_78_a0
ER  - 
%0 Journal Article
%A Gilbert Labelle
%T Binomial Species and Combinatorial Exponentiation
%J Séminaire lotharingien de combinatoire
%D 2018-2020
%V 78
%U http://geodesic.mathdoc.fr/item/SLC_2018-2020_78_a0/
%F SLC_2018-2020_78_a0

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We introduce a "binomial" species, B(X,Y)=(1+X)îY = E(Y Lg(1+X)), where E(X) is the species of finite sets and Lg(1+X) is the combinatorial logarithm. The expansion of B includes, by specialization of variables, the classical binomial expansion, binomial expansions for symmetric functions, and (q,t)-series. We also define and study a new exponentiation operation, F\,îG, between species.