Set maps, umbral calculus, and the chromatic polynomial

2005/07/03 by Gus Wiseman, Wiseman, Gus
Mathematics · #05A18 (Secondary) #05C15 (Primary) 05A40 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.math/0507038

openalex publication_date 2005/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=∑_{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.

Citations

• Acyclic orientations of graphs

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