UVic Discrete Math Seminar: Shayla Redlin Hume

Enumerating matroid extensions is a surprisingly difficult problem. One strategy is to relate extensions of certain matroids to stable sets in an auxiliary graph and use methods, like the container method, to count stable sets. In this talk, I will outline this strategy – after giving some matroid definitions and examples, of course. There will also be a short tutorial on the container method for graphs, which has many varied applications to other problems as well. By the end of the talk, we will see how the pieces of this counting strategy fit together and some results that come from it, including the incredible number of extensions that come from some very dense, symmetric matroids.