"Color structures and permutations":
We study color structures for tree level scattering amplitudes in gauge theory in order to determine the symmetry properties of the colorless sub-amplitudes. We determine the space of color structures together with the action of permutations of external legs on it, including characters and decomposition into irreps. Mathematically, free Lie algebras and the Lie operad are central. We discuss implications for the Parke-Taylor amplitudes and the recent Cachazo-He-Yuan amplitudes.