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A330374
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Triangle read by rows: T(n,k) is the number of partitions of n whose absolute value of Dyson's rank is equal to k, with 0 <= k < n.
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0
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1, 0, 2, 1, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 1, 4, 2, 2, 0, 2, 3, 2, 4, 2, 2, 0, 2, 2, 6, 4, 4, 2, 2, 0, 2, 4, 6, 6, 4, 4, 2, 2, 0, 2, 4, 10, 6, 8, 4, 4, 2, 2, 0, 2, 6, 10, 12, 6, 8, 4, 4, 2, 2, 0, 2, 7, 16, 12, 12, 8, 8, 4, 4, 2, 2, 0, 2, 11, 16, 18, 14, 12, 8, 8, 4, 4, 2, 2, 0, 2, 11, 26, 20, 20, 14, 14
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OFFSET
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1,3
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COMMENTS
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The rank of a partition is the largest part minus the number of parts.
Since the largest part of a partition equals the number of parts of its conjugate partition, so the rank of a partition also is equal to the difference between the number of parts of its conjugate partition and the number of parts of the partition.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
--------------------------------------------------------------------
n \ k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
--------------------------------------------------------------------
[ 1] 1;
[ 2] 0, 2;
[ 3] 1, 0, 2;
[ 4] 1, 2, 0, 2;
[ 5] 1, 2, 2, 0, 2;
[ 6] 1, 4, 2, 2, 0, 2;
[ 7] 3, 2, 4, 2, 2, 0, 2;
[ 8] 2, 6, 4, 4, 2, 2, 0, 2;
[ 9] 4, 6, 6, 4, 4, 2, 2, 0, 2;
[10] 4, 10, 6, 8, 4, 4, 2, 2, 0, 2;
[11] 6, 10, 12, 6, 8, 4, 4, 2, 2, 0, 2;
[12] 7, 16, 12, 12, 8, 8, 4, 4, 2, 2, 0, 2;
[13] 11, 16, 18, 14, 12, 8, 8, 4, 4, 2, 2, 0, 2;
[14] 11, 26, 20, 20, 14, 14, 8, 8, 4, 4, 2, 2, 0, 2;
[15] 16, 28, 30, 22, 22, 14, 14, 8, 8, 4, 4, 2, 2, 0, 2;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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