Set maps, umbral calculus, and the chromatic polynomial

Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying pS(x + y) = TU=S pT (x)pU (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 several new expansions of the chromatic polynomial. We also describe a set map generalization of Abel polynomials.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Gus Wiseman
• Keywords: Chromatic Polynomial, DM 2008, Polynomials, Set Map