SEMINAR: Groups and Combinatorics Seminar, Growth rates of binary matroids

Time and place: 3pm Friday 16 January in Weatherburn LT.

Speaker: Irene Pivotto (UWA)

Title: Growth rates of binary matroids.

Abstract: The growth rate of a class of matroids is a function of the rank which expresses how large a matroid in the class can be. For example, a planar graph on n vertices has at most 3n-6 edges. So the corresponding class of matroids has growth rate 3r-3 (since the rank of the matroid of a graph on n vertices is r=n-1). The Growth Rate Theorem says that any minor-closed class of matroids has growth rate that is either linear, quadratic or exponential (or undefined). This result is amazingly general, and thus it is of a qualitative nature. This talk focuses instead on the problem of determining the exact growth rate of some classes. In particular, I will discuss quadratic and linear growth rates in binary matroids. No prior knowledge of matroids is necessary.