Γ-species and the enumeration of unlabeled bipartite blocks

Counting unlabeled graphs is often surprisingly difficult, even with powerful generatingfunctionological tools. We'll present the theory of combinatorial species (and an extension dubbed 'Γ-species'), a category-theoretic framework for enumerative combinatorics which helps to resolve this difficulty. In particular, we'll illustrate how these theories can be used to count unlabeled bipartite blocks, a previously open problem. Despite occasional use of the word 'functor', this talk will be accessible to a general mathematical audience, including undergraduates. (This talk represents joint work with Ira M. Gessel at Brandeis University.)