1. Proofs & Confirmations The story of the
alternating sign matrix conjecture
David M. Bressoud
Macalester College
Hollins University
April 29, 2004

2. Institute for Defense Analysis
Bill Mills
Institute for Defense Analysis 1 –1
Howard Rumsey
Dave Robbins

3. Charles L. Dodgson aka Lewis Carroll1 –1
“Condensation of Determinants,” Proceedings of the Royal Society, London 1866

4. 1 –1

5. 1 –1
A5 = 429

6. 1 –1

7. 1 –1
Monotone Triangle

8. 1 –1
Monotone Triangle

9. 1 –1
12345

10. 1 –1 3
12345

11. 1 –1 2 3 2 4 3 2 5 4 2
12345

12. 1 –1 14 2 3 2 4 3 2 5 4 2
12345

13. 1 –1 7 14 14 7 23 26 14 23 14 7 2 3 2 4 3 2 5 4 2
12345

14. 1 –1
105 7 14 14 7 23 26 14 23 14 7 2 3 2 4 3 2 5 4 2
12345

15. 1 –1 42
105
135
105 42 7 14 14 7 23 26 14 23 14 7 2 3 2 4 3 2 5 4 2
12345

16. 429 1 –1 42
105
135
105 42 7 14 14 7 23 26 14 23 14 7 2 3 2 4 3 2 5 4 2
12345

17. 1 –1
A5 = 429
A10 = 129, 534, 272, 700

18. 1 –1
A5 = 429
A10 = 129, 534, 272, 700
A20 =
= 1.43… 1045