Chromatic sums of general maps on the sphere and the projective plane
The chromatic sum function of a class of rooted maps is the sum of the chromatic polynomials of all these maps with a given root-vertex degree, root-face degree and number of edges, non-root vertices and non-root faces, multiplied by a monomial in five variables that enumerate these parameters. Authors' absstract: We study the chromatic sum functions of rooted general maps on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of rooted loopless maps, bipartite maps and Eulerian maps are also derived. Moreover, some explicit expressions of enumerating functions are also derived. Reviewer's remark: Among these explicit expressions are formulas for the number of rooted loopless maps, bipartite maps and Eulerian maps on the sphere. These three formulas are already in the literature, but only the first one is given a citation in this article.
scientific article; zbMATH DE number 5121350
scientific article