Chromatic polynomials of partition systems
The authors develop a generalization of chromatic polynomials to certain set systems called partition systems (the independent subsets of a graph form a partition system where their polynomial specializes to the classical chromatic polynomial). This also generalizes the umbral chromatic polynomial in the context of the Roman-Rota umbral calculus. The authors have in mind applications to algebraic topology and formal group laws, but this paper concentrates on combinatorial aspects, proving various identities involving these polynomials and generalizations of properties of the classical chromatic polynomial. Partition systems with a group action are also considered.
scientific article; zbMATH DE number 1018531
scientific article