All-Orders Singular Emission in Gauge Theories

I present a class of functions unifying all singular limits for the emission of soft or collinear gluons in gauge-theory amplitudes at any order in perturbation theory. Each function is a generalization of the antenna functions of previous works. The helicity-summed interferences of these functions are thereby also generalizations to higher orders of the Catani-Seymour dipole factorization function.