1. On the number of matroids Nikhil Bansal (TU Eindhoven) Rudi Pendavingh (TU Eindhoven) Jorn van der Pol (TU Eindhoven)

2. Matroids

3. Narrowing the gap m(n) Better bound

4. Known results

5. Our Result

6. Outline Knuth’s lower bound construction Counting stable sets The final upper bound

7. Knuth’s Lower bound

8. Knuth’s bound

9. Rest of the talk

10. Bounding s(n)

11. Better Bound

12. Our Result

13. Rest of the talk Encoding for independent sets. Encoding for Matroids.

14. A useful lemma A

15. Encoding a stable set S G I A

20. Phases: d 1 2 d-1 …

21. Encoding Matroids

24. Finish up

25. Questions

26. Thank You

27. Narrowing the gap

28. Encoding Matroids

29. Finish up

30. Knuth’s Lower bound B B B’