Combinatorial Structure

Let be a Ring containing . Let be the Category of finite sets and bijections between them. Let be the Category whose objects are pairs where is a finite set and is a function and Morphisms in are bijections such that .

A combinatorial structure is a Functor The map is called the weight function. We may write just when the context is clear.

Often for all . When weight is not specified, we assume that this is the case.

Unlabelled Structure Ordinary Generating Function Exponential Generating Function Combinatorial Union Combinatorial Product Combinatorial Composition Unlabelled Composition Finite Sequence Set Structure Combinatorial Derivative Rooted Structure