Geodesic
Decomposable Functors and the Exponential Principle, II
Séminaire lotharingien de combinatoire, 61A (2009-2011) 
Peter J. Cameron; Christian Krattenthaler; Thomas W. Müller. Decomposable Functors and the Exponential Principle, II. Séminaire lotharingien de combinatoire, 61A (2009-2011). http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a12/
@article{SLC_2009-2011_61A_a12,
     author = {Peter J. Cameron and Christian Krattenthaler and Thomas W. M\"uller},
     title = {Decomposable {Functors} and the {Exponential} {Principle,} {II}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2009-2011},
     volume = {61A},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a12/}
}
TY  - JOUR
AU  - Peter J. Cameron
AU  - Christian Krattenthaler
AU  - Thomas W. Müller
TI  - Decomposable Functors and the Exponential Principle, II
JO  - Séminaire lotharingien de combinatoire
PY  - 2009-2011
VL  - 61A
UR  - http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a12/
ID  - SLC_2009-2011_61A_a12
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%0 Journal Article
%A Peter J. Cameron
%A Christian Krattenthaler
%A Thomas W. Müller
%T Decomposable Functors and the Exponential Principle, II
%J Séminaire lotharingien de combinatoire
%D 2009-2011
%V 61A
%U http://geodesic.mathdoc.fr/item/SLC_2009-2011_61A_a12/
%F SLC_2009-2011_61A_a12

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

We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural transformations (composition operators), and we show that, somewhat surprisingly, a single axiom for the composition already suffices to guarantee validity of the exponential formula. We provide various illustrations of our theory, among which are applications to the enumeration of (semi-)magic squares.