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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001814
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(load all 3 compositions to match this statistic)
St001814: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 2
[2]
=> 3
[1,1]
=> 2
[3]
=> 4
[2,1]
=> 4
[1,1,1]
=> 2
[4]
=> 5
[3,1]
=> 6
[2,2]
=> 3
[2,1,1]
=> 4
[1,1,1,1]
=> 2
[5]
=> 6
[4,1]
=> 8
[3,2]
=> 6
[3,1,1]
=> 6
[2,2,1]
=> 4
[2,1,1,1]
=> 4
[1,1,1,1,1]
=> 2
[6]
=> 7
[5,1]
=> 10
[4,2]
=> 9
[4,1,1]
=> 8
[3,3]
=> 4
[3,2,1]
=> 8
[3,1,1,1]
=> 6
[2,2,2]
=> 3
[2,2,1,1]
=> 4
[2,1,1,1,1]
=> 4
[1,1,1,1,1,1]
=> 2
[7]
=> 8
[6,1]
=> 12
[5,2]
=> 12
[5,1,1]
=> 10
[4,3]
=> 8
[4,2,1]
=> 12
[4,1,1,1]
=> 8
[3,3,1]
=> 6
[3,2,2]
=> 6
[3,2,1,1]
=> 8
[3,1,1,1,1]
=> 6
[2,2,2,1]
=> 4
[2,2,1,1,1]
=> 4
[2,1,1,1,1,1]
=> 4
[1,1,1,1,1,1,1]
=> 2
[8]
=> 9
[7,1]
=> 14
[6,2]
=> 15
[6,1,1]
=> 12
[5,3]
=> 12
[5,2,1]
=> 16
Description
The number of partitions interlacing the given partition.
Matching statistic: St000708
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 23% ●values known / values provided: 40%●distinct values known / distinct values provided: 23%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 23% ●values known / values provided: 40%●distinct values known / distinct values provided: 23%
Values
[1]
=> 10 => [1,2] => [2,1]
=> 2
[2]
=> 100 => [1,3] => [3,1]
=> 3
[1,1]
=> 110 => [1,1,2] => [2,1,1]
=> 2
[3]
=> 1000 => [1,4] => [4,1]
=> 4
[2,1]
=> 1010 => [1,2,2] => [2,2,1]
=> 4
[1,1,1]
=> 1110 => [1,1,1,2] => [2,1,1,1]
=> 2
[4]
=> 10000 => [1,5] => [5,1]
=> 5
[3,1]
=> 10010 => [1,3,2] => [3,2,1]
=> 6
[2,2]
=> 1100 => [1,1,3] => [3,1,1]
=> 3
[2,1,1]
=> 10110 => [1,2,1,2] => [2,2,1,1]
=> 4
[1,1,1,1]
=> 11110 => [1,1,1,1,2] => [2,1,1,1,1]
=> 2
[5]
=> 100000 => [1,6] => [6,1]
=> 6
[4,1]
=> 100010 => [1,4,2] => [4,2,1]
=> 8
[3,2]
=> 10100 => [1,2,3] => [3,2,1]
=> 6
[3,1,1]
=> 100110 => [1,3,1,2] => [3,2,1,1]
=> 6
[2,2,1]
=> 11010 => [1,1,2,2] => [2,2,1,1]
=> 4
[2,1,1,1]
=> 101110 => [1,2,1,1,2] => [2,2,1,1,1]
=> 4
[1,1,1,1,1]
=> 111110 => [1,1,1,1,1,2] => [2,1,1,1,1,1]
=> 2
[6]
=> 1000000 => [1,7] => [7,1]
=> 7
[5,1]
=> 1000010 => [1,5,2] => [5,2,1]
=> 10
[4,2]
=> 100100 => [1,3,3] => [3,3,1]
=> 9
[4,1,1]
=> 1000110 => [1,4,1,2] => [4,2,1,1]
=> 8
[3,3]
=> 11000 => [1,1,4] => [4,1,1]
=> 4
[3,2,1]
=> 101010 => [1,2,2,2] => [2,2,2,1]
=> 8
[3,1,1,1]
=> 1001110 => [1,3,1,1,2] => [3,2,1,1,1]
=> 6
[2,2,2]
=> 11100 => [1,1,1,3] => [3,1,1,1]
=> 3
[2,2,1,1]
=> 110110 => [1,1,2,1,2] => [2,2,1,1,1]
=> 4
[2,1,1,1,1]
=> 1011110 => [1,2,1,1,1,2] => [2,2,1,1,1,1]
=> 4
[1,1,1,1,1,1]
=> 1111110 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1]
=> 2
[7]
=> 10000000 => [1,8] => [8,1]
=> 8
[6,1]
=> 10000010 => [1,6,2] => [6,2,1]
=> 12
[5,2]
=> 1000100 => [1,4,3] => [4,3,1]
=> 12
[5,1,1]
=> 10000110 => [1,5,1,2] => [5,2,1,1]
=> 10
[4,3]
=> 101000 => [1,2,4] => [4,2,1]
=> 8
[4,2,1]
=> 1001010 => [1,3,2,2] => [3,2,2,1]
=> 12
[4,1,1,1]
=> 10001110 => [1,4,1,1,2] => [4,2,1,1,1]
=> 8
[3,3,1]
=> 110010 => [1,1,3,2] => [3,2,1,1]
=> 6
[3,2,2]
=> 101100 => [1,2,1,3] => [3,2,1,1]
=> 6
[3,2,1,1]
=> 1010110 => [1,2,2,1,2] => [2,2,2,1,1]
=> 8
[3,1,1,1,1]
=> 10011110 => [1,3,1,1,1,2] => [3,2,1,1,1,1]
=> 6
[2,2,2,1]
=> 111010 => [1,1,1,2,2] => [2,2,1,1,1]
=> 4
[2,2,1,1,1]
=> 1101110 => [1,1,2,1,1,2] => [2,2,1,1,1,1]
=> 4
[2,1,1,1,1,1]
=> 10111110 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1]
=> 4
[1,1,1,1,1,1,1]
=> 11111110 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1]
=> 2
[8]
=> 100000000 => [1,9] => [9,1]
=> 9
[7,1]
=> 100000010 => [1,7,2] => [7,2,1]
=> 14
[6,2]
=> 10000100 => [1,5,3] => [5,3,1]
=> 15
[6,1,1]
=> 100000110 => [1,6,1,2] => [6,2,1,1]
=> 12
[5,3]
=> 1001000 => [1,3,4] => [4,3,1]
=> 12
[5,2,1]
=> 10001010 => [1,4,2,2] => [4,2,2,1]
=> 16
[11]
=> 100000000000 => ? => ?
=> ? = 12
[10,1]
=> 100000000010 => ? => ?
=> ? = 20
[9,1,1]
=> 100000000110 => ? => ?
=> ? = 18
[8,3]
=> 1000001000 => ? => ?
=> ? = 24
[8,2,1]
=> 10000001010 => [1,7,2,2] => ?
=> ? = 28
[8,1,1,1]
=> 100000001110 => ? => ?
=> ? = 16
[7,2,2]
=> 1000001100 => ? => ?
=> ? = 18
[7,1,1,1,1]
=> 100000011110 => ? => ?
=> ? = 14
[6,3,1,1]
=> 1000100110 => ? => ?
=> ? = 24
[6,2,2,1]
=> 1000011010 => ? => ?
=> ? = 20
[6,1,1,1,1,1]
=> 100000111110 => [1,6,1,1,1,1,2] => ?
=> ? = 12
[5,3,1,1,1]
=> 1001001110 => [1,3,3,1,1,2] => ?
=> ? = 18
[5,2,2,1,1]
=> 1000110110 => [1,4,1,2,1,2] => ?
=> ? = 16
[5,2,1,1,1,1]
=> 10001011110 => [1,4,2,1,1,1,2] => ?
=> ? = 16
[5,1,1,1,1,1,1]
=> 100001111110 => ? => ?
=> ? = 10
[4,3,1,1,1,1]
=> 1010011110 => ? => ?
=> ? = 12
[4,1,1,1,1,1,1,1]
=> 100011111110 => ? => ?
=> ? = 8
[3,3,1,1,1,1,1]
=> 1100111110 => ? => ?
=> ? = 6
[3,2,2,1,1,1,1]
=> 1011011110 => ? => ?
=> ? = 8
[3,2,1,1,1,1,1,1]
=> 10101111110 => [1,2,2,1,1,1,1,1,2] => ?
=> ? = 8
[3,1,1,1,1,1,1,1,1]
=> 100111111110 => ? => ?
=> ? = 6
[2,2,2,1,1,1,1,1]
=> 1110111110 => [1,1,1,2,1,1,1,1,2] => ?
=> ? = 4
[2,1,1,1,1,1,1,1,1,1]
=> 101111111110 => ? => ?
=> ? = 4
[1,1,1,1,1,1,1,1,1,1,1]
=> 111111111110 => ? => ?
=> ? = 2
[12]
=> 1000000000000 => ? => ?
=> ? = 13
[11,1]
=> 1000000000010 => ? => ?
=> ? = 22
[10,2]
=> 100000000100 => [1,9,3] => ?
=> ? = 27
[10,1,1]
=> 1000000000110 => ? => ?
=> ? = 20
[9,3]
=> 10000001000 => ? => ?
=> ? = 28
[8,3,1]
=> 10000010010 => ? => ?
=> ? = 36
[8,2,2]
=> 10000001100 => ? => ?
=> ? = 21
[8,2,1,1]
=> 100000010110 => ? => ?
=> ? = 28
[8,1,1,1,1]
=> 1000000011110 => ? => ?
=> ? = 16
[7,4,1]
=> 1000100010 => ? => ?
=> ? = 32
[6,4,1,1]
=> 1001000110 => [1,3,4,1,2] => ?
=> ? = 24
[6,3,1,1,1]
=> 10001001110 => ? => ?
=> ? = 24
[6,2,2,2]
=> 1000011100 => [1,5,1,1,3] => ?
=> ? = 15
[6,2,2,1,1]
=> 10000110110 => ? => ?
=> ? = 20
[6,2,1,1,1,1]
=> 100001011110 => [1,5,2,1,1,1,2] => ?
=> ? = 20
[6,1,1,1,1,1,1]
=> 1000001111110 => ? => ?
=> ? = 12
[5,4,1,1,1]
=> 1010001110 => [1,2,4,1,1,2] => ?
=> ? = 16
[5,3,2,1,1]
=> 1001010110 => [1,3,2,2,1,2] => ?
=> ? = 24
[5,3,1,1,1,1]
=> 10010011110 => ? => ?
=> ? = 18
[5,2,2,2,1]
=> 1000111010 => [1,4,1,1,2,2] => ?
=> ? = 16
[5,2,2,1,1,1]
=> 10001101110 => ? => ?
=> ? = 16
[5,2,1,1,1,1,1]
=> 100010111110 => ? => ?
=> ? = 16
[5,1,1,1,1,1,1,1]
=> 1000011111110 => ? => ?
=> ? = 10
[4,3,1,1,1,1,1]
=> 10100111110 => ? => ?
=> ? = 12
[3,3,1,1,1,1,1,1]
=> 11001111110 => [1,1,3,1,1,1,1,1,2] => ?
=> ? = 6
[3,2,2,1,1,1,1,1]
=> 10110111110 => ? => ?
=> ? = 8
Description
The product of the parts of an integer partition.
Matching statistic: St001232
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 6%
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 6%
Values
[1]
=> [1,0,1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1 = 2 - 1
[2]
=> [1,1,0,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,1,0,0]
=> 2 = 3 - 1
[1,1]
=> [1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1 = 2 - 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 4 - 1
[2,1]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 4 - 1
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4 = 5 - 1
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? = 6 - 1
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2 = 3 - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ? = 4 - 1
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1 = 2 - 1
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5 = 6 - 1
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? = 8 - 1
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? = 6 - 1
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 6 - 1
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 4 - 1
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? = 4 - 1
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1 = 2 - 1
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 6 = 7 - 1
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 10 - 1
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ? = 9 - 1
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ? = 8 - 1
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 4 - 1
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 8 - 1
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ? = 6 - 1
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2 = 3 - 1
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ? = 4 - 1
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 4 - 1
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1 = 2 - 1
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> ? = 8 - 1
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 12 - 1
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 12 - 1
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 10 - 1
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? = 8 - 1
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? = 12 - 1
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? = 8 - 1
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ? = 6 - 1
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ? = 6 - 1
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? = 8 - 1
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> ? = 6 - 1
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? = 4 - 1
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> ? = 4 - 1
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 4 - 1
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> ? = 2 - 1
[8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> ? = 9 - 1
[7,1]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? = 14 - 1
[6,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 15 - 1
[6,1,1]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 12 - 1
[5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> ? = 12 - 1
[5,2,1]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ? = 16 - 1
[5,1,1,1]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> ? = 10 - 1
[4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4 = 5 - 1
[4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? = 12 - 1
[4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? = 9 - 1
[4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? = 12 - 1
[4,1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ? = 8 - 1
[3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? = 6 - 1
[3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 6 - 1
[3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? = 8 - 1
[3,2,1,1,1]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? = 8 - 1
[3,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 6 - 1
[2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2 = 3 - 1
[2,2,2,1,1]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> ? = 4 - 1
[2,2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 4 - 1
[2,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 4 - 1
[1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? = 2 - 1
[3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3 = 4 - 1
[5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 5 = 6 - 1
[2,2,2,2,2]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2 = 3 - 1
[4,4,4]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 4 = 5 - 1
[3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3 = 4 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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