- FindStat

Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001312
(load all 2 compositions to match this statistic)

Mapping

St001312: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,1] => 2 = 1 + 1
[2] => 1 = 0 + 1
[1,1,1] => 5 = 4 + 1
[1,2] => 3 = 2 + 1
[2,1] => 3 = 2 + 1
[3] => 1 = 0 + 1
[1,1,1,1] => 14 = 13 + 1
[1,1,2] => 9 = 8 + 1
[1,2,1] => 10 = 9 + 1
[1,3] => 4 = 3 + 1
[2,1,1] => 9 = 8 + 1
[2,2] => 6 = 5 + 1
[3,1] => 4 = 3 + 1
[4] => 1 = 0 + 1
[1,1,1,1,1] => 42 = 41 + 1
[1,1,1,2] => 28 = 27 + 1
[1,1,2,1] => 32 = 31 + 1
[1,1,3] => 14 = 13 + 1
[1,2,1,1] => 32 = 31 + 1
[1,2,2] => 22 = 21 + 1
[1,3,1] => 17 = 16 + 1
[1,4] => 5 = 4 + 1
[2,1,1,1] => 28 = 27 + 1
[2,1,2] => 19 = 18 + 1
[2,2,1] => 22 = 21 + 1
[2,3] => 10 = 9 + 1
[3,1,1] => 14 = 13 + 1
[3,2] => 10 = 9 + 1
[4,1] => 5 = 4 + 1
[5] => 1 = 0 + 1
[1,1,1,1,1,1] => 132 = 131 + 1
[1,1,1,1,2] => 90 = 89 + 1
[1,1,1,2,1] => 104 = 103 + 1
[1,1,1,3] => 48 = 47 + 1
[1,1,2,1,1] => 107 = 106 + 1
[1,1,2,2] => 75 = 74 + 1
[1,1,3,1] => 62 = 61 + 1
[1,1,4] => 20 = 19 + 1
[1,2,1,1,1] => 104 = 103 + 1
[1,2,1,2] => 72 = 71 + 1
[1,2,2,1] => 84 = 83 + 1
[1,2,3] => 40 = 39 + 1
[1,3,1,1] => 62 = 61 + 1
[1,3,2] => 45 = 44 + 1
[1,4,1] => 26 = 25 + 1
[1,5] => 6 = 5 + 1
[2,1,1,1,1] => 90 = 89 + 1
[2,1,1,2] => 62 = 61 + 1
[2,1,2,1] => 72 = 71 + 1
[2,1,3] => 34 = 33 + 1

Description

Number of parabolic noncrossing partitions indexed by the composition. Also the number of elements in the

$\nu$ -Tamari lattice with

$\nu = \nu_\alpha = 1^{\alpha_1} 0^{\alpha_1} \cdots 1^{\alpha_k} 0^{\alpha_k}$ , the bounce path indexed by the composition

$\alpha$ . These elements are Dyck paths weakly above the bounce path

$\nu_\alpha$ .

Matching statistic: St000419
(load all 6 compositions to match this statistic)

Mapping

Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000419: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,1] => [1,0,1,0]
 => 1
[2] => [1,1,0,0]
 => 0
[1,1,1] => [1,0,1,0,1,0]
 => 4
[1,2] => [1,0,1,1,0,0]
 => 2
[2,1] => [1,1,0,0,1,0]
 => 2
[3] => [1,1,1,0,0,0]
 => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0]
 => 13
[1,1,2] => [1,0,1,0,1,1,0,0]
 => 8
[1,2,1] => [1,0,1,1,0,0,1,0]
 => 9
[1,3] => [1,0,1,1,1,0,0,0]
 => 3
[2,1,1] => [1,1,0,0,1,0,1,0]
 => 8
[2,2] => [1,1,0,0,1,1,0,0]
 => 5
[3,1] => [1,1,1,0,0,0,1,0]
 => 3
[4] => [1,1,1,1,0,0,0,0]
 => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => 41
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => 27
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => 31
[1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => 13
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => 31
[1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 21
[1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 16
[1,4] => [1,0,1,1,1,1,0,0,0,0]
 => 4
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => 27
[2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 18
[2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 21
[2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 9
[3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 13
[3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 9
[4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 4
[5] => [1,1,1,1,1,0,0,0,0,0]
 => 0
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 131
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 89
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 103
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 47
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 106
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
 => 74
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 61
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 19
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 103
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => 71
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 83
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 39
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 61
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 44
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 25
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 5
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 89
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 61
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 71
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 33

Description

The number of Dyck paths that are weakly above the Dyck path, except for the path itself.

Matching statistic: St000420
(load all 6 compositions to match this statistic)

Mapping

Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000420: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,1] => [1,0,1,0]
 => 2 = 1 + 1
[2] => [1,1,0,0]
 => 1 = 0 + 1
[1,1,1] => [1,0,1,0,1,0]
 => 5 = 4 + 1
[1,2] => [1,0,1,1,0,0]
 => 3 = 2 + 1
[2,1] => [1,1,0,0,1,0]
 => 3 = 2 + 1
[3] => [1,1,1,0,0,0]
 => 1 = 0 + 1
[1,1,1,1] => [1,0,1,0,1,0,1,0]
 => 14 = 13 + 1
[1,1,2] => [1,0,1,0,1,1,0,0]
 => 9 = 8 + 1
[1,2,1] => [1,0,1,1,0,0,1,0]
 => 10 = 9 + 1
[1,3] => [1,0,1,1,1,0,0,0]
 => 4 = 3 + 1
[2,1,1] => [1,1,0,0,1,0,1,0]
 => 9 = 8 + 1
[2,2] => [1,1,0,0,1,1,0,0]
 => 6 = 5 + 1
[3,1] => [1,1,1,0,0,0,1,0]
 => 4 = 3 + 1
[4] => [1,1,1,1,0,0,0,0]
 => 1 = 0 + 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => 42 = 41 + 1
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => 28 = 27 + 1
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => 32 = 31 + 1
[1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => 14 = 13 + 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => 32 = 31 + 1
[1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 22 = 21 + 1
[1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 17 = 16 + 1
[1,4] => [1,0,1,1,1,1,0,0,0,0]
 => 5 = 4 + 1
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => 28 = 27 + 1
[2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 19 = 18 + 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 22 = 21 + 1
[2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 10 = 9 + 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 14 = 13 + 1
[3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 10 = 9 + 1
[4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 5 = 4 + 1
[5] => [1,1,1,1,1,0,0,0,0,0]
 => 1 = 0 + 1
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 132 = 131 + 1
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 90 = 89 + 1
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 104 = 103 + 1
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 48 = 47 + 1
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 107 = 106 + 1
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
 => 75 = 74 + 1
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 62 = 61 + 1
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 20 = 19 + 1
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 104 = 103 + 1
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => 72 = 71 + 1
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 84 = 83 + 1
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 40 = 39 + 1
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 62 = 61 + 1
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 45 = 44 + 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 26 = 25 + 1
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 6 = 5 + 1
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 90 = 89 + 1
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 62 = 61 + 1
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 72 = 71 + 1
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 34 = 33 + 1

Description

The number of Dyck paths that are weakly above a Dyck path.

Matching statistic: St000108
(load all 2 compositions to match this statistic)

Mapping

Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000108: Integer partitions ⟶ ℤResult quality: 17% ●values known / values provided: 20%●distinct values known / distinct values provided: 17%

Values

[1,1] => [1,0,1,0]
 => [1]
 => 2 = 1 + 1
[2] => [1,1,0,0]
 => []
 => 1 = 0 + 1
[1,1,1] => [1,0,1,0,1,0]
 => [2,1]
 => 5 = 4 + 1
[1,2] => [1,0,1,1,0,0]
 => [1,1]
 => 3 = 2 + 1
[2,1] => [1,1,0,0,1,0]
 => [2]
 => 3 = 2 + 1
[3] => [1,1,1,0,0,0]
 => []
 => 1 = 0 + 1
[1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 14 = 13 + 1
[1,1,2] => [1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 9 = 8 + 1
[1,2,1] => [1,0,1,1,0,0,1,0]
 => [3,1,1]
 => 10 = 9 + 1
[1,3] => [1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 4 = 3 + 1
[2,1,1] => [1,1,0,0,1,0,1,0]
 => [3,2]
 => 9 = 8 + 1
[2,2] => [1,1,0,0,1,1,0,0]
 => [2,2]
 => 6 = 5 + 1
[3,1] => [1,1,1,0,0,0,1,0]
 => [3]
 => 4 = 3 + 1
[4] => [1,1,1,1,0,0,0,0]
 => []
 => 1 = 0 + 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => 42 = 41 + 1
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => 28 = 27 + 1
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => 32 = 31 + 1
[1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => 14 = 13 + 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => 32 = 31 + 1
[1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => 22 = 21 + 1
[1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => 17 = 16 + 1
[1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => 5 = 4 + 1
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => 28 = 27 + 1
[2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => 19 = 18 + 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => 22 = 21 + 1
[2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 10 = 9 + 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => 14 = 13 + 1
[3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => 10 = 9 + 1
[4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [4]
 => 5 = 4 + 1
[5] => [1,1,1,1,1,0,0,0,0,0]
 => []
 => 1 = 0 + 1
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1]
 => ? = 131 + 1
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => ? = 89 + 1
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => ? = 103 + 1
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2,1]
 => ? = 47 + 1
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2,1]
 => ? = 106 + 1
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2,1]
 => ? = 74 + 1
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [5,2,2,2,1]
 => ? = 61 + 1
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2,1]
 => 20 = 19 + 1
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,1]
 => ? = 103 + 1
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [4,4,3,1,1]
 => ? = 71 + 1
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [5,3,3,1,1]
 => ? = 83 + 1
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [3,3,3,1,1]
 => ? = 39 + 1
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,1,1]
 => ? = 61 + 1
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [4,4,1,1,1]
 => ? = 44 + 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [5,1,1,1,1]
 => 26 = 25 + 1
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => 6 = 5 + 1
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2]
 => ? = 89 + 1
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2]
 => ? = 61 + 1
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2]
 => ? = 71 + 1
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2]
 => ? = 33 + 1
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2]
 => ? = 74 + 1
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2]
 => ? = 52 + 1
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [5,2,2,2]
 => ? = 44 + 1
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => 15 = 14 + 1
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [5,4,3]
 => ? = 47 + 1
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [4,4,3]
 => ? = 33 + 1
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [5,3,3]
 => ? = 39 + 1
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3,3]
 => 20 = 19 + 1
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [5,4]
 => 20 = 19 + 1
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => 15 = 14 + 1
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [5]
 => 6 = 5 + 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => []
 => 1 = 0 + 1
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,2,1]
 => ? = 428 + 1
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [5,5,4,3,2,1]
 => ? = 296 + 1
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [6,4,4,3,2,1]
 => ? = 344 + 1
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [4,4,4,3,2,1]
 => ? = 164 + 1
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [6,5,3,3,2,1]
 => ? = 358 + 1
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [5,5,3,3,2,1]
 => ? = 254 + 1
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [6,3,3,3,2,1]
 => ? = 218 + 1
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [3,3,3,3,2,1]
 => ? = 74 + 1
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [6,5,4,2,2,1]
 => ? = 358 + 1
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [5,5,4,2,2,1]
 => ? = 251 + 1
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [6,4,4,2,2,1]
 => ? = 294 + 1
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [4,4,4,2,2,1]
 => ? = 144 + 1
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [6,5,2,2,2,1]
 => ? = 232 + 1
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [5,5,2,2,2,1]
 => ? = 170 + 1
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [6,2,2,2,2,1]
 => ? = 106 + 1
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2,2,1]
 => ? = 26 + 1
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,1,1]
 => ? = 344 + 1
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [5,5,4,3,1,1]
 => ? = 240 + 1
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [6,4,4,3,1,1]
 => ? = 280 + 1
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [4,4,4,3,1,1]
 => ? = 136 + 1
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [6,5,3,3,1,1]
 => ? = 294 + 1
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [5,5,3,3,1,1]
 => ? = 210 + 1
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [6,3,3,3,1,1]
 => ? = 184 + 1
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [3,3,3,3,1,1]
 => ? = 64 + 1
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [6,5,4,1,1,1]
 => ? = 218 + 1
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => [5,5,4,1,1,1]
 => ? = 156 + 1
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [6,4,4,1,1,1]
 => ? = 184 + 1
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1]
 => 7 = 6 + 1
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2,2]
 => 21 = 20 + 1
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [5,5]
 => 21 = 20 + 1
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6]
 => 7 = 6 + 1
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => []
 => 1 = 0 + 1
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1]
 => 8 = 7 + 1

Description

The number of partitions contained in the given partition.