If *F*(*x*) and *G*(*x*) are formal power series with *G*(0) = 0, then we have seen (after Proposition 1.1.9) that the composition *F*(*G*(*x*)) is a well-defined formal power series. In this chapter we will investigate the combinatorial ramifications of power series composition. In this section we will be concerned with the case where *F*(*x*) and *G*(*x*) are exponential generating functions, and especially the case *F*(*x*) = *e ^{x}*.

Let us first consider the combinatorial significance of the product *F*(*x*)*G*(*x*) of two exponential generating functions

Throughout this chapter *K* denotes a field of characteristic ...

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