Set Structure

The Combinatorial Structure defined by

Lemma

Ordinary Generating Function is:

Exponential Generating Function is:

Lemma

Let be a Combinatorial Structure. The Combinatorial Composition is building the structure on each class of every partition of .

Proof

As in the definition of Combinatorial Composition, let and . Each of these contributes to the disjoint union, i.e. one unique element. Thus every partition of contributes exactly elements. This is exactly what we needed.