1 / 47

On zero-sum problems

Joseph DiMuro, 12/6/11. On zero-sum problems. An introductory challenge. A zero-sum problem. A zero-sum problem. Outline. Definitions from abstract algebra The zero-sum problem for general groups Variations of the zero-sum problem An application of zero-sum problems.

jeneil
Download Presentation

On zero-sum problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Joseph DiMuro, 12/6/11 On zero-sum problems

  2. An introductory challenge

  3. A zero-sum problem

  4. A zero-sum problem

  5. Outline • Definitions from abstract algebra • The zero-sum problem for general groups • Variations of the zero-sum problem • An application of zero-sum problems

  6. Finite abelian groups

  7. Finite abelian groups

  8. Other finite abelian groups

  9. The Davenport constant

  10. Isomorphic abelian groups

  11. Isomorphic abelian groups

  12. Isomorphic abelian groups

  13. Isomorphic abelian groups Generators:

  14. Isomorphic abelian groups

  15. Isomorphic abelian groups

  16. Isomorphic abelian groups

  17. Isomorphic abelian groups Finite abelian groups may always be written as direct products of groups of prime power order

  18. Isomorphic abelian groups

  19. The general zero-sum problem

  20. A variation

  21. A variation

  22. A new challenge

  23. A simple lower bound

  24. Erdös,Ginzburg,Ziv Theorem

  25. Generalizing EGV

  26. Generalizing EGV

  27. Other variations

  28. An application of zero-sum problems • Zero-sum problems were used to show that there are infinitely many Carmichael numbers

  29. Fermat’s “little” theorem

  30. Pseudoprimes

  31. Carmichael numbers

  32. Carmichael numbers

  33. Infinitely many Carmichael numbers

  34. References Any questions?

More Related