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Proofs & Confirmations The story of the alternating sign matrix conjecture

Follow the journey of proving the Alternating Sign Matrix Conjecture through confirmation and intricate mathematical analysis by David M. Bressoud and other researchers. Explore the historical connection to Lewis Carroll's work and the Royal Society publication. Witness the mathematical beauty of the Monotone Triangle.

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Proofs & Confirmations The story of the alternating sign matrix conjecture

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

  2. Bill Mills Institute for Defense Analysis 1 0 0 –1 1 0 –1 0 1 Howard Rumsey Dave Robbins

  3. Charles L. Dodgson aka Lewis Carroll 1 0 0 –1 1 0 –1 0 1 “Condensation of Determinants,” Proceedings of the Royal Society, London 1866

  4. 1 0 0 –1 1 0 –1 0 1

  5. 1 0 0 –1 1 0 –1 0 1 A5 = 429

  6. 1 0 0 –1 1 0 –1 0 1

  7. 1 0 0 –1 1 0 –1 0 1 Monotone Triangle

  8. 1 0 0 –1 1 0 –1 0 1 Monotone Triangle

  9. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 12 13 14 15 23 24 25 34 35 45 123 124 125 134 135 145 234 235 345 1234 1235 1245 1345 2345 12345

  10. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 12 13 14 15 23 24 25 34 35 45 123 124 125 134 135 145 234 235 345 3 1234 1235 1245 1345 2345 12345

  11. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 12 13 14 15 23 24 25 34 35 45 123 124 125 134 135 145 234 235 345 2 3 2 4 3 2 5 4 2 1234 1235 1245 1345 2345 12345

  12. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 12 13 14 15 23 24 25 34 35 45 14 123 124 125 134 135 145 234 235 345 2 3 2 4 3 2 5 4 2 1234 1235 1245 1345 2345 12345

  13. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 12 13 14 15 23 24 25 34 35 45 7 14 14 7 23 26 14 23 14 7 123 124 125 134 135 145 234 235 345 2 3 2 4 3 2 5 4 2 1234 1235 1245 1345 2345 12345

  14. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 105 12 13 14 15 23 24 25 34 35 45 7 14 14 7 23 26 14 23 14 7 123 124 125 134 135 145 234 235 345 2 3 2 4 3 2 5 4 2 1234 1235 1245 1345 2345 12345

  15. 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 42 105 135 105 42 12 13 14 15 23 24 25 34 35 45 7 14 14 7 23 26 14 23 14 7 123 124 125 134 135 145 234 235 345 2 3 2 4 3 2 5 4 2 1234 1235 1245 1345 2345 12345

  16. 429 1 2 3 4 5 1 0 0 –1 1 0 –1 0 1 42 105 135 105 42 12 13 14 15 23 24 25 34 35 45 7 14 14 7 23 26 14 23 14 7 123 124 125 134 135 145 234 235 345 2 3 2 4 3 2 5 4 2 1234 1235 1245 1345 2345 12345

  17. 1 0 0 –1 1 0 –1 0 1 A5 = 429 A10 = 129, 534, 272, 700

  18. 1 0 0 –1 1 0 –1 0 1 A5 = 429 A10 = 129, 534, 272, 700 A20 = 1436038934715538200913155682637051204376827212 = 1.43… 1045

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