This material has been published in Séminaire Lotharingien Combin. 61A (2011), Article 61Am, 38 pages, the only definitive repository of the content that has been certified and accepted after peer review.

Peter J. Cameron, Christian Krattenthaler and Thomas W. Müller

Decomposable functors and the exponential principle, II

(36 pages)

Abstract. 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 and cubes.

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