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EXAMPLE
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Triangle begins:
[1];
[2], [1,1];
[3], [2,1], [1,1,1];
[4], [3,1], [2,2], [2,1,1], [1,1,1,1];
[5], [4,1], [3,2], [3,1,1], [2,2,1], [2,1,1,1], [1,1,1,1,1];
[6], [5,1], [4,2], [4,1,1], [3,3], [3,2,1], [2,2,2], [3,1,1,1], [2,2,1,1], ...
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For n = 9 the 9th row of the triangle contains the partitions ordered as shown below:
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Ranks
Conjugate
Label with label Partition k = 1 2 3 4 5 6 7 8 9
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1 30 [9] 8 -1 -1 -1 -1 -1 -1 -1 -1
2 29 [8, 1] 6 0 -1 -1 -1 -1 -1 -1 0
3 28 [7, 2] 5 0 -1 -1 -1 -1 -1 0 0
4 27 [7, 1, 1] 4 0 0 -1 -1 -1 -1 0 0
5 26 [6, 3] 4 1 -2 -1 -1 -1 0 0 0
6 25 [6, 2, 1] 3 0 0 -1 -1 -1 0 0 0
7 24 [6, 1, 1, 1] 2 0 0 0 -1 -1 0 0 0
8 23 [5, 4] 3 2 -2 -2 -1 0 0 0 0
9 22 [5, 3, 1] 2 1 -1 -1 -1 0 0 0 0
10 21 [5, 2, 2] 2 -1 1 -1 -1 0 0 0 0
11 20 [5, 2, 1, 1] 1 0 0 0 -1 0 0 0 0
12 19 [4, 4, 1] 1 2 -1 -2 0 0 0 0 0
13 18 [4, 3, 2] 1 0 0 -1 0 0 0 0 0
14 17 [4, 3, 1, 1] 0 1 -1 0 0 0 0 0 0
15 (self-conjugate) [5, 1, 1, 1, 1] All zeros -> 0 0 0 0 0 0 0 0 0
16 (self-conjugate) [3, 3, 3] All zeros -> 0 0 0 0 0 0 0 0 0
17 14 [4, 2, 2, 1] 0 -1 1 0 0 0 0 0 0
18 13 [3, 3, 2, 1] -1 0 0 1 0 0 0 0 0
19 12 [3, 2, 2, 2] -1 -2 1 2 0 0 0 0 0
20 11 [4, 2, 1, 1, 1] -1 0 0 0 1 0 0 0 0
21 10 [3, 3, 1, 1, 1] -2 1 -1 1 1 0 0 0 0
22 9 [3, 2, 2, 1, 1] -2 -1 1 1 1 0 0 0 0
23 8 [2, 2, 2, 2, 1] -3 -2 2 2 1 0 0 0 0
24 7 [4, 1, 1, 1, 1, 1] -2 0 0 0 1 1 0 0 0
25 6 [3, 2, 1, 1, 1, 1] -3 0 0 1 1 1 0 0 0
26 5 [2, 2, 2, 1, 1, 1] -4 -1 2 1 1 1 0 0 0
27 4 [3, 1, 1, 1, 1, 1, 1] -4 0 0 1 1 1 1 0 0
28 3 [2, 2, 1, 1, 1, 1, 1] -5 0 1 1 1 1 1 0 0
29 2 [2, 1, 1, 1, 1, 1, 1, 1] -6 0 1 1 1 1 1 1 0
30 1 [1, 1, 1, 1, 1, 1, 1, 1, 1] -8 1 1 1 1 1 1 1 1
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