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