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Statistic identifier: St000049
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Collection: Integer partitions
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Description: The number of set partitions whose sorted block sizes correspond to the partition.
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References:
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Code:
def statistic(L):
return len( [ S for S in SetPartitions(L.size()) if S.to_partition() == L ] )
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Statistic values:
[] => 1
[1] => 1
[2] => 1
[1,1] => 1
[3] => 1
[2,1] => 3
[1,1,1] => 1
[4] => 1
[3,1] => 4
[2,2] => 3
[2,1,1] => 6
[1,1,1,1] => 1
[5] => 1
[4,1] => 5
[3,2] => 10
[3,1,1] => 10
[2,2,1] => 15
[2,1,1,1] => 10
[1,1,1,1,1] => 1
[6] => 1
[5,1] => 6
[4,2] => 15
[4,1,1] => 15
[3,3] => 10
[3,2,1] => 60
[3,1,1,1] => 20
[2,2,2] => 15
[2,2,1,1] => 45
[2,1,1,1,1] => 15
[1,1,1,1,1,1] => 1
[7] => 1
[6,1] => 7
[5,2] => 21
[5,1,1] => 21
[4,3] => 35
[4,2,1] => 105
[4,1,1,1] => 35
[3,3,1] => 70
[3,2,2] => 105
[3,2,1,1] => 210
[3,1,1,1,1] => 35
[2,2,2,1] => 105
[2,2,1,1,1] => 105
[2,1,1,1,1,1] => 21
[1,1,1,1,1,1,1] => 1
[8] => 1
[7,1] => 8
[6,2] => 28
[6,1,1] => 28
[5,3] => 56
[5,2,1] => 168
[5,1,1,1] => 56
[4,4] => 35
[4,3,1] => 280
[4,2,2] => 210
[4,2,1,1] => 420
[4,1,1,1,1] => 70
[3,3,2] => 280
[3,3,1,1] => 280
[3,2,2,1] => 840
[3,2,1,1,1] => 560
[3,1,1,1,1,1] => 56
[2,2,2,2] => 105
[2,2,2,1,1] => 420
[2,2,1,1,1,1] => 210
[2,1,1,1,1,1,1] => 28
[1,1,1,1,1,1,1,1] => 1
[9] => 1
[8,1] => 9
[7,2] => 36
[7,1,1] => 36
[6,3] => 84
[6,2,1] => 252
[6,1,1,1] => 84
[5,4] => 126
[5,3,1] => 504
[5,2,2] => 378
[5,2,1,1] => 756
[5,1,1,1,1] => 126
[4,4,1] => 315
[4,3,2] => 1260
[4,3,1,1] => 1260
[4,2,2,1] => 1890
[4,2,1,1,1] => 1260
[4,1,1,1,1,1] => 126
[3,3,3] => 280
[3,3,2,1] => 2520
[3,3,1,1,1] => 840
[3,2,2,2] => 1260
[3,2,2,1,1] => 3780
[3,2,1,1,1,1] => 1260
[3,1,1,1,1,1,1] => 84
[2,2,2,2,1] => 945
[2,2,2,1,1,1] => 1260
[2,2,1,1,1,1,1] => 378
[2,1,1,1,1,1,1,1] => 36
[1,1,1,1,1,1,1,1,1] => 1
[10] => 1
[9,1] => 10
[8,2] => 45
[8,1,1] => 45
[7,3] => 120
[7,2,1] => 360
[7,1,1,1] => 120
[6,4] => 210
[6,3,1] => 840
[6,2,2] => 630
[6,2,1,1] => 1260
[6,1,1,1,1] => 210
[5,5] => 126
[5,4,1] => 1260
[5,3,2] => 2520
[5,3,1,1] => 2520
[5,2,2,1] => 3780
[5,2,1,1,1] => 2520
[5,1,1,1,1,1] => 252
[4,4,2] => 1575
[4,4,1,1] => 1575
[4,3,3] => 2100
[4,3,2,1] => 12600
[4,3,1,1,1] => 4200
[4,2,2,2] => 3150
[4,2,2,1,1] => 9450
[4,2,1,1,1,1] => 3150
[4,1,1,1,1,1,1] => 210
[3,3,3,1] => 2800
[3,3,2,2] => 6300
[3,3,2,1,1] => 12600
[3,3,1,1,1,1] => 2100
[3,2,2,2,1] => 12600
[3,2,2,1,1,1] => 12600
[3,2,1,1,1,1,1] => 2520
[3,1,1,1,1,1,1,1] => 120
[2,2,2,2,2] => 945
[2,2,2,2,1,1] => 4725
[2,2,2,1,1,1,1] => 3150
[2,2,1,1,1,1,1,1] => 630
[2,1,1,1,1,1,1,1,1] => 45
[1,1,1,1,1,1,1,1,1,1] => 1
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Created: Mar 25, 2013 at 10:03 by Christian Stump
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Last Updated: Oct 29, 2017 at 20:28 by Martin Rubey