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Published byAlice Stone Modified over 6 years ago
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n 1 2 3 4 5 6 7 8 9 An 42 429 7436 218348 = 2 3 7 = 3 11 13 = 22 11 132 = 22 132 17 19 = 23 13 172 192 = 22 5 172 193 23 1 –1
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n 1 2 3 4 5 6 7 8 9 An 42 429 7436 218348 very suspicious 1 –1 = 2 3 7 = 3 11 13 = 22 11 132 = 22 132 17 19 = 23 13 172 192 = 22 5 172 193 23
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There is exactly one 1 in the first row
2 3 4 5 6 7 8 9 An 42 429 7436 218348 There is exactly one 1 in the first row 1 –1
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There is exactly one 1 in the first row
2 3 4 5 6 7 8 9 An 1+1 2+3+2 … There is exactly one 1 in the first row 1 –1
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1 1 –1
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There is exactly one 1 in the first row
2 3 4 5 6 7 8 9 An 1+1 2+3+2 … 1 –1
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There is exactly one 1 in the first row
2 3 4 5 6 7 8 9 An 1+1 2+3+2 … 1 –1
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1 1 –1 + + +
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1 1 –1 + + +
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1 1 2/2 1 2 2/ /2 2 7 2/ /2 7 42 2/ /2 42 429 2/ /2 429 1 –1
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1 1 2/2 1 2 2/ /2 2 7 2/ / /2 7 42 2/ / / /2 42 429 2/ / / / /2 429 1 –1
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2/2 2/ /2 2/ / /2 2/ / / /2 2/ / / / /2 1 –1
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1+1 1+2 1+1 2+3 1+3 1+1 3+4 3+6 1+4 1+1 4+5 6+10 4+10 1+5 Numerators:
1 –1
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Numerators: 1+1 1+1 1+2 1+1 2+3 1+3 1+1 3+4 3+6 1+4
Numerators: 1 –1 Conjecture 1:
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Conjecture 2 (corollary of Conjecture 1):
–1 Conjecture 2 (corollary of Conjecture 1):
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1 –1 Richard Stanley M.I.T.
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George Andrews, Penn State
1 –1 Richard Stanley M.I.T. Andrews’ Theorem: the number of descending plane partitions of size n is George Andrews, Penn State
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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 –1
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What is a descending plane partition?
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 –1 What is a descending plane partition?
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