  This thesis addresses a number of enumerative problems that arise in the
context of quantum field theory and in the process of renormalization. In
particular, the enumeration of rooted connected chord diagrams is further
studied and new applications in quenched QED and Yukawa theories are
introduced. Chord diagrams appear in quantum field theory in the context of
Dyson-Schwinger equations, where, according to recent results, they are used to
express the solutions. In another direction, we study the action of point field
diffeomorphisms on a free theory. We give a new proof of a vanishing phenomenon
for tree-level amplitudes of the transformed theories.
