  Some important properties of the chromatic polynomial also hold for any
polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using
umbral calculus, we give a formula for the expansion of such a set map in terms
of any polynomial sequence of binomial type. This leads to some new expansions
of the chromatic polynomial. We also describe a set map generalization of Abel
polynomials.

Combinatorics