Department of Mathematics
Homepages
(hier geht es zur ggf. vollständigeren Homepage im alten Layout)
(this way to the possibly more complete Homepage in the old layout)
(this way to the possibly more complete Homepage in the old layout)
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 |