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Statistic identifier: St000108
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Collection: Integer partitions
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Description: The number of partitions contained in the given partition.
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References:
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Code:
def statistic(L):
return sum( 1 for n in range(L.size()) for P in Partitions(n) if L.contains(P) ) + 1
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Statistic values:
[] => 1
[1] => 2
[2] => 3
[1,1] => 3
[3] => 4
[2,1] => 5
[1,1,1] => 4
[4] => 5
[3,1] => 7
[2,2] => 6
[2,1,1] => 7
[1,1,1,1] => 5
[5] => 6
[4,1] => 9
[3,2] => 9
[3,1,1] => 10
[2,2,1] => 9
[2,1,1,1] => 9
[1,1,1,1,1] => 6
[6] => 7
[5,1] => 11
[4,2] => 12
[4,1,1] => 13
[3,3] => 10
[3,2,1] => 14
[3,1,1,1] => 13
[2,2,2] => 10
[2,2,1,1] => 12
[2,1,1,1,1] => 11
[1,1,1,1,1,1] => 7
[7] => 8
[6,1] => 13
[5,2] => 15
[5,1,1] => 16
[4,3] => 14
[4,2,1] => 19
[4,1,1,1] => 17
[3,3,1] => 16
[3,2,2] => 16
[3,2,1,1] => 19
[3,1,1,1,1] => 16
[2,2,2,1] => 14
[2,2,1,1,1] => 15
[2,1,1,1,1,1] => 13
[1,1,1,1,1,1,1] => 8
[8] => 9
[7,1] => 15
[6,2] => 18
[6,1,1] => 19
[5,3] => 18
[5,2,1] => 24
[5,1,1,1] => 21
[4,4] => 15
[4,3,1] => 23
[4,2,2] => 22
[4,2,1,1] => 26
[4,1,1,1,1] => 21
[3,3,2] => 19
[3,3,1,1] => 22
[3,2,2,1] => 23
[3,2,1,1,1] => 24
[3,1,1,1,1,1] => 19
[2,2,2,2] => 15
[2,2,2,1,1] => 18
[2,2,1,1,1,1] => 18
[2,1,1,1,1,1,1] => 15
[1,1,1,1,1,1,1,1] => 9
[9] => 10
[8,1] => 17
[7,2] => 21
[7,1,1] => 22
[6,3] => 22
[6,2,1] => 29
[6,1,1,1] => 25
[5,4] => 20
[5,3,1] => 30
[5,2,2] => 28
[5,2,1,1] => 33
[5,1,1,1,1] => 26
[4,4,1] => 25
[4,3,2] => 28
[4,3,1,1] => 32
[4,2,2,1] => 32
[4,2,1,1,1] => 33
[4,1,1,1,1,1] => 25
[3,3,3] => 20
[3,3,2,1] => 28
[3,3,1,1,1] => 28
[3,2,2,2] => 25
[3,2,2,1,1] => 30
[3,2,1,1,1,1] => 29
[3,1,1,1,1,1,1] => 22
[2,2,2,2,1] => 20
[2,2,2,1,1,1] => 22
[2,2,1,1,1,1,1] => 21
[2,1,1,1,1,1,1,1] => 17
[1,1,1,1,1,1,1,1,1] => 10
[10] => 11
[9,1] => 19
[8,2] => 24
[8,1,1] => 25
[7,3] => 26
[7,2,1] => 34
[7,1,1,1] => 29
[6,4] => 25
[6,3,1] => 37
[6,2,2] => 34
[6,2,1,1] => 40
[6,1,1,1,1] => 31
[5,5] => 21
[5,4,1] => 34
[5,3,2] => 37
[5,3,1,1] => 42
[5,2,2,1] => 41
[5,2,1,1,1] => 42
[5,1,1,1,1,1] => 31
[4,4,2] => 31
[4,4,1,1] => 35
[4,3,3] => 30
[4,3,2,1] => 42
[4,3,1,1,1] => 41
[4,2,2,2] => 35
[4,2,2,1,1] => 42
[4,2,1,1,1,1] => 40
[4,1,1,1,1,1,1] => 29
[3,3,3,1] => 30
[3,3,2,2] => 31
[3,3,2,1,1] => 37
[3,3,1,1,1,1] => 34
[3,2,2,2,1] => 34
[3,2,2,1,1,1] => 37
[3,2,1,1,1,1,1] => 34
[3,1,1,1,1,1,1,1] => 25
[2,2,2,2,2] => 21
[2,2,2,2,1,1] => 25
[2,2,2,1,1,1,1] => 26
[2,2,1,1,1,1,1,1] => 24
[2,1,1,1,1,1,1,1,1] => 19
[1,1,1,1,1,1,1,1,1,1] => 11
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Created: Jun 15, 2013 at 13:18 by Christian Stump
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Last Updated: Oct 29, 2017 at 16:05 by Martin Rubey