Set maps, umbral calculus, and the chromatic polynomial

Details Set maps, umbral calculus, and the chromatic polynomial Set maps, umbral calculus, and the chromatic polynomial

2005-07-03

arxiv.org/abs/math/0507038v2

Mathematics

Combinatorics

20 pages

Scientific paper

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.

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