Decomposable functors and the exponential principle, II

Details Decomposable functors and the exponential principle, II Decomposable functors and the exponential principle, II

2009-11-19

arxiv.org/abs/0911.3760v2

S\'eminaire Lotharingien Combin. 61A (2011), Article B61Am, 38 pages

Mathematics

Combinatorics

38 pages, AmS-LaTeX; seriously revised: the relation of this work with prior work of Mat\'i as Menni on an exponential princip

Scientific paper

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.

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