Matroids

In this talk, we will discuss the definition of matroids and their properties. As alluded to in previous talks, matroids generalize the notion of linear independence of subsets of some ambient set. We will discuss some examples of matroids and recipes to get them from more concrete objects. Furthermore, we will define terms such as basis, spanning sets, rank, and flats, as well as the associated lattice of flats of a matroid, generalizing ideas like the intersection poset from the theory of hyperplane arrangements.

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Date published: Wednesday, September 18, 2024