Contraction theorem for the algebraic reduction of (anti)commutators involving operator strings

Abstract
A proof by induction is given of the so-called contraction theorem for the evaluation of (anti)commutators of strings of Fermion creation and annihilation operators. This theorem bears some formal similarity to Wick's theorem but is essentially simpler and its applications do not lead to any disconnected diagrams. Examples of applications to configuration-interaction and coupled-cluster methods are presented.