Set maps, umbral calculus, and the chromatic polynomial
Abstract
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying pS(x+y)=ΣT U=SpT(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 some new expansions of the chromatic polynomial. We also describe a set map generalization of Abel polynomials.
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