What Is... Seminar

Marcelo AguiarCornell University
What is a species?

Wednesday, December 4, 2013 - 5:30pm
Malott 207

Classical combinatorics organizes cardinalities into generating functions. After Joyal, one may similarly organize sets into species. We will discuss this notion and illustrate its usefulness by means of one or two basic enumerative applications. Sets may carry algebraic structures, such as that of a group. Species may carry analogous structures. We will discuss groups and rings in species. This aspect of the theory goes beyond enumeration. We will focus on an understanding and generalization of the chromatic polynomial which exploits the ring structure of the species of graphs.