EAN: 9783319117126

SPRINGERBRIEFS IN MATHEMATICS SET OPERADS IN ...

This monograph has two main objectives. The first one is to give a self-contained exposition of
the relevant facts about set operads  in the context of combinatorial species and its
operations. This approach has various advantages: one of them is that the definition of
combinatorial operations on species  product  sum  substitution and derivative  are simple and
natural. They were designed as the set theoretical counterparts of the homonym operations on
exponential generating functions  giving an immediate insight on the combinatorial meaning of
them. The second objective is more ambitious. Before formulating it  authors present a brief
historic account on the sources of decomposition theory. For more than forty years
decompositions of discrete structures have been studied in different branches of discrete
mathematics: combinatorial optimization  network and graph theory  switching design or boolean
functions  simple multi-person games and clutters  etc.

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