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Proofs & Confirmations The story of the alternating sign matrix conjecture. David M. Bressoud Macalester College. Hollins University April 29, 2004. Bill Mills. Institute for Defense Analysis. 1 0 0 –1 1 0 –1 0 1. Howard Rumsey. Dave Robbins. Charles L. Dodgson

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Presentation Transcript
slide1

Proofs & Confirmations

The story of the

alternating sign matrix conjecture

David M. Bressoud

Macalester College

Hollins University

April 29, 2004

slide2

Bill Mills

Institute for Defense Analysis

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Howard Rumsey

Dave Robbins

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Charles L. Dodgson

aka Lewis Carroll

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“Condensation of Determinants,” Proceedings of the Royal Society, London 1866

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A5 = 429

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Monotone Triangle

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Monotone Triangle

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123 124 125 134 135 145 234 235 345

1234 1235 1245 1345 2345

12345

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1234 1235 1245 1345 2345

12345

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1234 1235 1245 1345 2345

12345

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1234 1235 1245 1345 2345

12345

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1234 1235 1245 1345 2345

12345

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1234 1235 1245 1345 2345

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429

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1234 1235 1245 1345 2345

12345

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A5 = 429

A10 = 129, 534, 272, 700

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A5 = 429

A10 = 129, 534, 272, 700

A20 = 1436038934715538200913155682637051204376827212

= 1.43… 1045