Fachbereich Mathematik 
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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:

Sheet 1

Sheet 2

Sheet 3

Sheet 4

Sheet 5

Sheet 6

Sheet 7

Sheet 8

Sheet 9

Sheet 10

Sheet 11

Sheet 12

Sheet 13

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


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

  Seitenanfang  Impress 2017-01-31, Nathan Bowler