Fachbereich Mathematik
FachbereichMathematik
There will be one exercise sheet per week.
Here are the exercise sheets:
week 1
week 2
week 3
week 4
week 5
week 6
week 7
week 8
week 9
week 10
week 11
week 12
For information on finite matroids, see `Matroid Theory' by James Oxley. Papers about infinite matroids can be found here. The website for a previous version of this course is here.
2.4 | Overview, independence and basis axioms, basic examples |
7.4 | Other axiomatisations: circuits, closure etc. |
9.4 | Duality, definition of minors |
14.4 | Bases, independent sets and circuits of minors |
16.4 | Union and Intersection |
21.4 | The theorems of König, Hall and Menger |
23.4 | Scrawl systems and basic examples, duality |
28.4 | Minors of scrawl systems and algebraic cycle systems |
30.4 | Bases in scrawl systems, examples of hereditarily based systems |
5.5 | Equivalence of the axiomatisations |
7.5 | Definition of |G| |
12.5 | Properties of |G|, topological circuits |
19.5 | Topological circuits are circuits of M_{FB}* |
21.5 | Connectivity |
26.5 | 2-Connectivity and torsos |
28.5 | Submodularity and trees of separations |
9.6 | The canonical tree decomposition into circuits, cocircuits and 3-connected torsos |
11.6 | The linking conjecture and the theorem of Aharoni and Berger |
16.6 | The Intersection, Packing/Covering and Covering conjectures |
18.6 | Proofs of special cases of the Covering and Linking Conjectures |
23.6 | Thin sums representability, quasibinary wild matroids |
25.6 | Properties of tame binary matroids |
30.6 | Affine compactness, paintability and representability |
02.7 | Excluded minors for representability, truncation. |