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A280319
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Irregular triangle read by rows: T(m, n) is the n-th permutation of m things generated by the Steinhaus-Johnson-Trotter algorithm, represented by row number of A055089.
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2
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0, 0, 1, 0, 2, 3, 5, 4, 1, 0, 6, 8, 9, 15, 14, 12, 2, 3, 13, 16, 17, 23, 22, 19, 5, 4, 18, 20, 21, 11, 10, 7, 1, 0, 24, 30, 32, 33, 57, 56, 54, 48, 6, 8, 50, 60, 62, 63, 65, 64, 61, 51, 9, 15, 75, 85, 88, 89, 87, 86, 84, 74, 14, 12, 72, 78, 80, 81
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OFFSET
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0,5
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COMMENTS
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Row m is a permutation of the integers 0..m!-1, so this is a triangle in which row m>=1 has length A000142(m).
Compare A280318 for Heap's algorithm, which is one infinite permutation rather than a triangle of finite permutations.
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LINKS
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EXAMPLE
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Triangle begins:
m/n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1 0
2 0 1
3 0 2 3 5 4 1
4 0 6 8 9 15 14 12 2 3 13 16 17 23 22 19 5 4 18 20 21 11 10 7 1
Example for row m=4. On the right are the permutations of {1,2,3,4} in the order generated by the Steinhaus-Johnson-Trotter algorithm (A207324):
n rev colex T(4,n) SJT
0 1 2 3 4 0 1 2 3 4
1 2 1 3 4 6 1 2 4 3
2 1 3 2 4 8 1 4 2 3
3 3 1 2 4 9 4 1 2 3
4 2 3 1 4 15 4 1 3 2
5 3 2 1 4 14 1 4 3 2
6 1 2 4 3 12 1 3 4 2
7 2 1 4 3 2 1 3 2 4
8 1 4 2 3 3 3 1 2 4
9 4 1 2 3 13 3 1 4 2
10 2 4 1 3 16 3 4 1 2
11 4 2 1 3 17 4 3 1 2
12 1 3 4 2 23 4 3 2 1
13 3 1 4 2 22 3 4 2 1
14 1 4 3 2 19 3 2 4 1
15 4 1 3 2 5 3 2 1 4
16 3 4 1 2 4 2 3 1 4
17 4 3 1 2 18 2 3 4 1
18 2 3 4 1 20 2 4 3 1
19 3 2 4 1 21 4 2 3 1
20 2 4 3 1 11 4 2 1 3
21 4 2 3 1 10 2 4 1 3
22 3 4 2 1 7 2 1 4 3
23 4 3 2 1 1 2 1 3 4
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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