Combinatorial species

Summary

A combinatorial species is a rule that assigns to each finite set the structures of a given kind on it, see the definition. The rule must be compatible with renaming the elements, which makes it a functor on finite sets and bijections. Each species has an exponential generating function, and operations on species match operations on these series. The theory was introduced by André Joyal and gives a conceptual basis for the symbolic method for labelled structures.