ul 2 00 5 Set maps , umbral calculus , and the chromatic
نویسنده
چکیده
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying pS(x + y) = ∑ T⊎U=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.
منابع مشابه
Set maps, umbral calculus, and the chromatic polynomial
In order to motivate our results we will begin by describing two classical expansions of the chromatic polynomial. Let G be a simple graph with finite vertex set V . Let χG(x) be the number of proper colorings of G with x colors (assignments of colors 1, 2, . . . , x to the vertices of G so that no two adjacent vertices have the same color). If e is an edge of G, let G\e be G with e removed, an...
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تاریخ انتشار 2005