1 / 19

1 0 0 –1 1 0 –1 0 1

n 1 2 3 4 5 6 7 8 9. A n 1 2 7 42 429 7436 218348 10850216 911835460. = 2  3  7. = 3  11  13. = 2 2  11  13 2. = 2 2  13 2  17  19. = 2 3  13  17 2  19 2. = 2 2  5  17 2  19 3  23. 1 0 0 –1 1 0 –1 0 1. n 1 2 3 4 5 6 7 8 9. A n 1

candice
Download Presentation

1 0 0 –1 1 0 –1 0 1

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. n 1 2 3 4 5 6 7 8 9 An 1 2 7 42 429 7436 218348 10850216 911835460 = 2  3  7 = 3  11  13 = 22 11  132 = 22 132  17  19 = 23 13  172  192 = 22 5  172  193  23 1 0 0 –1 1 0 –1 0 1

  2. n 1 2 3 4 5 6 7 8 9 An 1 2 7 42 429 7436 218348 10850216 911835460 very suspicious 1 0 0 –1 1 0 –1 0 1 = 2  3  7 = 3  11  13 = 22 11  132 = 22 132  17  19 = 23 13  172  192 = 22 5  172  193  23

  3. n 1 2 3 4 5 6 7 8 9 An 1 2 7 42 429 7436 218348 10850216 911835460 There is exactly one 1 in the first row 1 0 0 –1 1 0 –1 0 1

  4. n 1 2 3 4 5 6 7 8 9 An 1 1+1 2+3+2 7+14+14+7 42+105+… There is exactly one 1 in the first row 1 0 0 –1 1 0 –1 0 1

  5. 1 1 1 2 3 2 7 14 14 7 42 105 135 105 42 429 1287 2002 2002 1287 429 1 0 0 –1 1 0 –1 0 1

  6. There is exactly one 1 in the first row n 1 2 3 4 5 6 7 8 9 An 1 1+1 2+3+2 7+14+14+7 42+105+… 1 0 0 –1 1 0 –1 0 1

  7. There is exactly one 1 in the first row n 1 2 3 4 5 6 7 8 9 An 1 1+1 2+3+2 7+14+14+7 42+105+… 1 0 0 –1 1 0 –1 0 1

  8. 1 1 1 2 3 2 7 14 14 7 42 105 135 105 42 429 1287 2002 2002 1287 429 1 0 0 –1 1 0 –1 0 1 + + +

  9. 1 1 1 2 3 2 7 14 14 7 42 105 135 105 42 429 1287 2002 2002 1287 429 1 0 0 –1 1 0 –1 0 1 + + +

  10. 1 1 2/2 1 2 2/3 3 3/2 2 7 2/4 14 14 4/2 7 42 2/5 105 135 105 5/2 42 429 2/6 1287 2002 2002 1287 6/2 429 1 0 0 –1 1 0 –1 0 1

  11. 1 1 2/2 1 2 2/3 3 3/2 2 7 2/4 14 5/5 14 4/2 7 42 2/5 105 7/9 135 9/7 105 5/2 42 429 2/6 1287 9/14 2002 16/16 2002 14/9 1287 6/2 429 1 0 0 –1 1 0 –1 0 1

  12. 2/2 2/33/2 2/45/54/2 2/57/99/75/2 2/69/1416/1614/96/2 1 0 0 –1 1 0 –1 0 1

  13. Numerators: 1+1 1+11+2 1+12+31+3 1+13+43+61+4 1+14+56+104+101+5 1 0 0 –1 1 0 –1 0 1

  14. 1+1 1+11+2 1+12+31+3 1+13+43+61+4 1+14+56+104+101+5 Numerators: 1 0 0 –1 1 0 –1 0 1 Conjecture 1:

  15. Conjecture 1: 1 0 0 –1 1 0 –1 0 1 Conjecture 2 (corollary of Conjecture 1):

  16. 1 0 0 –1 1 0 –1 0 1 Richard Stanley M.I.T.

  17. 1 0 0 –1 1 0 –1 0 1 Richard Stanley M.I.T. Andrews’ Theorem: the number of descending plane partitions of size n is George Andrews, Penn State

  18. All you have to do is find a 1-to-1 correspondence between n by n alternating sign matrices and descending plane partitions of size n, and conjecture 2 will be proven! 1 0 0 –1 1 0 –1 0 1

  19. All you have to do is find a 1-to-1 correspondence between n by n alternating sign matrices and descending plane partitions of size n, and conjecture 2 will be proven! 1 0 0 –1 1 0 –1 0 1 What is a descending plane partition?

More Related