On properties of almost all matroids

Seongmin Ok (옥성민)

Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark

Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark

2016/02/12

**Fri**4PM-5PMIn this talk, I attempt to provide a comprehensive introduction to the matroid properties that hold for almost all matroids.

Welsh conjectured that almost all matroids are paving, open for nearly 50 years. If true, the properties of paving matroids translate to almost all matroids, such as non-representability, concentrated ranks, high connectivity and so on. We shall see the related properties that are shown to hold for almost all matroids with some of the proofs. An overview of recent progress and possible further directions will also be presented.

Welsh conjectured that almost all matroids are paving, open for nearly 50 years. If true, the properties of paving matroids translate to almost all matroids, such as non-representability, concentrated ranks, high connectivity and so on. We shall see the related properties that are shown to hold for almost all matroids with some of the proofs. An overview of recent progress and possible further directions will also be presented.