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## Nathan Bowler

### Lecture course "Matroid Theory", winter semester 2016/17

#### Exercise sheets

There will be one exercise sheet per week.

Here are the exercise sheets:

#### Background material:

Lucas Wansner kindly provided his lecture notes for the first 3 chapters of the course. The course is based on the book `Matroid Theory' by James Oxley. We will only discuss finite matroids

#### Log:

 18.10. Independent sets and bases 20.10. Circuits and rank 25.10. Closure operators and geometric representations 27.10. Duality: definition and basic properties 01.11. Duals of representable matroids 03.11. Duals of graphic matroids 08.11. Minors 10.11. Minors of representable and graphic matroids 15.11. Connectivity, definition of direct sum 17.11. Properties of direct sum, n-connectivity 22.11. Connectivity of graphic matroids 24.11. 2-Sums 29.11. Decomposition over 2-separations 01.12. 3-connected matroids 06.12. Binary matroids 08.12. Determinants and Grassmann-Plücker Functions 13.12. Regular representations 15.12. Regular matroids 20.12. Excluded minors for regular matroids 22.12. Sums of represented matroids 10.01. Wheels and whirls 12.01. The Splitter Theorem 17.01. Applications of the Splitter Theorem, 3-sums 19.01. 3-sums, minimal nongraphic matroids 24.01. Grafts 26.01. Excluded minors for the class of graphic matroids 31.01. 3-separations due to R_12, proof of the decomposition theorem 02.02. the union and intersection theorems

 Impress 2017-01-31, Nathan Bowler