Séminaire Lotharingien de Combinatoire, B61Am (2010), 38 pp.
Peter J. Cameron, Christian Krattenthaler and Thomas W. Müller
Decomposable Functors and the Exponential Principle, II
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.
Received: December 12, 2009.
Revised: December 13, 2010.
Accepted: January 20, 2011.
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