Combinatorial Functional Equations: Basic Theory

This monograph, consisting of two books, I and II, includes fresh approaches in the two branches of combinatorics and functional equations, concentrating on algebraic approaches to establishing a rigorous theory for discussing the property of being well- defined and solutions for which it is not necessary to care about convergence or non- convergence and suitability. Its central feature is in building up a theory for unifying the theories of counting distinct classes in classifications under a variety of isomor- phisms on a variety of combinatorial congurations, particularly maps (rooted and un-rooted), embeddings of graphs on surfaces, even graphs themselves and so forth, with an infinite partition vector as given parameter.