A master identity for homotopy Gerstenhaber algebras

We produce a master identity {m}{m}=0 for homotopy Gerstenhaber algebras, as defined by Getzler and Jones and utilized by Kimura, Voronov, and Zuckerman in the context of topological conformal field theories. To this end, we introduce the notion of a "partitioned multilinear map" and explain the mechanics of composing such maps. In addition, many new examples of pre-Lie algebras and homotopy Gerstenhaber algebras are given.