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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