Identifier
- St000049: Integer partitions ⟶ ℤ
Values
=>
Cc0002;cc-rep
[]=>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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Description
The number of set partitions whose sorted block sizes correspond to the partition.
Code
def statistic(L): return len( [ S for S in SetPartitions(L.size()) if S.to_partition() == L ] )
Created
Mar 25, 2013 at 10:03 by Christian Stump
Updated
Oct 29, 2017 at 20:28 by Martin Rubey
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