  We introduce a novel approach to compute Compton amplitudes involving a
fermion pair inspired by Hopf algebra amplitude constructions. This approach
features a recursive relation employing quasi-shuffle sets, directly verifiable
by massive factorization properties. We derive results for minimal gauge
invariant color-kinematic numerators with physical massive poles using this
method. We have also deduced a graphical method for deriving numerators that
simplifies the numerator generation and eliminates redundancies, thus providing
several computational advantages.
