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.
Cite
@article{arxiv.0911.3760,
title = {Decomposable functors and the exponential principle, II},
author = {Peter Cameron and Christian Krattenthaler and Thomas W. Müller},
journal= {arXiv preprint arXiv:0911.3760},
year = {2011}
}
Comments
38 pages, AmS-LaTeX; seriously revised: the relation of this work with prior work of Mat\'i as Menni on an exponential principle in the framework of symmetric monoidal categories is clarified; a section on higher-dimensional magic cubes has been put into the separate paper "A note on higher-dimensional magic matrices"; journal version