All Split Helicity Tree-Level Gluon Amplitudes

Recently a new recursion relation for tree-level gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of zigzag diagrams. We comment on generalizations of this result.