Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000290
(load all 3 compositions to match this statistic)
Mapping
Mp00095: Integer partitions —to binary word⟶ Binary words
St000290: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 10 => 1
[2]
 => 100 => 1
[1,1]
 => 110 => 2
[3]
 => 1000 => 1
[2,1]
 => 1010 => 4
[1,1,1]
 => 1110 => 3
[4]
 => 10000 => 1
[3,1]
 => 10010 => 5
[2,2]
 => 1100 => 2
[2,1,1]
 => 10110 => 5
[1,1,1,1]
 => 11110 => 4
[5]
 => 100000 => 1
[4,1]
 => 100010 => 6
[3,2]
 => 10100 => 4
[3,1,1]
 => 100110 => 6
[2,2,1]
 => 11010 => 6
[2,1,1,1]
 => 101110 => 6
[1,1,1,1,1]
 => 111110 => 5
[6]
 => 1000000 => 1
[5,1]
 => 1000010 => 7
[4,2]
 => 100100 => 5
[4,1,1]
 => 1000110 => 7
[3,3]
 => 11000 => 2
[3,2,1]
 => 101010 => 9
[3,1,1,1]
 => 1001110 => 7
[2,2,2]
 => 11100 => 3
[2,2,1,1]
 => 110110 => 7
[2,1,1,1,1]
 => 1011110 => 7
[1,1,1,1,1,1]
 => 1111110 => 6
[7]
 => 10000000 => 1
[6,1]
 => 10000010 => 8
[5,2]
 => 1000100 => 6
[5,1,1]
 => 10000110 => 8
[4,3]
 => 101000 => 4
[4,2,1]
 => 1001010 => 11
[4,1,1,1]
 => 10001110 => 8
[3,3,1]
 => 110010 => 7
[3,2,2]
 => 101100 => 5
[3,2,1,1]
 => 1010110 => 10
[3,1,1,1,1]
 => 10011110 => 8
[2,2,2,1]
 => 111010 => 8
[2,2,1,1,1]
 => 1101110 => 8
[2,1,1,1,1,1]
 => 10111110 => 8
[1,1,1,1,1,1,1]
 => 11111110 => 7
[8]
 => 100000000 => 1
[7,1]
 => 100000010 => 9
[6,2]
 => 10000100 => 7
[6,1,1]
 => 100000110 => 9
[5,3]
 => 1001000 => 5
[5,2,1]
 => 10001010 => 13
Description
The major index of a binary word. This is the sum of the positions of descents, i.e., a one followed by a zero. For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Matching statistic: St000293
Mapping
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
St000293: Binary words ⟶ ℤResult quality: 92% ●values known / values provided: 92%●distinct values known / distinct values provided: 97%
Values
[1]
 => 10 => 10 => 1
[2]
 => 100 => 010 => 1
[1,1]
 => 110 => 110 => 2
[3]
 => 1000 => 0010 => 1
[2,1]
 => 1010 => 1100 => 4
[1,1,1]
 => 1110 => 1110 => 3
[4]
 => 10000 => 00010 => 1
[3,1]
 => 10010 => 10100 => 5
[2,2]
 => 1100 => 0110 => 2
[2,1,1]
 => 10110 => 11010 => 5
[1,1,1,1]
 => 11110 => 11110 => 4
[5]
 => 100000 => 000010 => 1
[4,1]
 => 100010 => 100100 => 6
[3,2]
 => 10100 => 01100 => 4
[3,1,1]
 => 100110 => 101010 => 6
[2,2,1]
 => 11010 => 11100 => 6
[2,1,1,1]
 => 101110 => 110110 => 6
[1,1,1,1,1]
 => 111110 => 111110 => 5
[6]
 => 1000000 => 0000010 => 1
[5,1]
 => 1000010 => 1000100 => 7
[4,2]
 => 100100 => 010100 => 5
[4,1,1]
 => 1000110 => 1001010 => 7
[3,3]
 => 11000 => 00110 => 2
[3,2,1]
 => 101010 => 111000 => 9
[3,1,1,1]
 => 1001110 => 1010110 => 7
[2,2,2]
 => 11100 => 01110 => 3
[2,2,1,1]
 => 110110 => 111010 => 7
[2,1,1,1,1]
 => 1011110 => 1101110 => 7
[1,1,1,1,1,1]
 => 1111110 => 1111110 => 6
[7]
 => 10000000 => 00000010 => 1
[6,1]
 => 10000010 => 10000100 => 8
[5,2]
 => 1000100 => 0100100 => 6
[5,1,1]
 => 10000110 => 10001010 => 8
[4,3]
 => 101000 => 001100 => 4
[4,2,1]
 => 1001010 => 1101000 => 11
[4,1,1,1]
 => 10001110 => 10010110 => 8
[3,3,1]
 => 110010 => 101100 => 7
[3,2,2]
 => 101100 => 011010 => 5
[3,2,1,1]
 => 1010110 => 1110010 => 10
[3,1,1,1,1]
 => 10011110 => 10101110 => 8
[2,2,2,1]
 => 111010 => 111100 => 8
[2,2,1,1,1]
 => 1101110 => 1110110 => 8
[2,1,1,1,1,1]
 => 10111110 => 11011110 => 8
[1,1,1,1,1,1,1]
 => 11111110 => 11111110 => 7
[8]
 => 100000000 => 000000010 => 1
[7,1]
 => 100000010 => 100000100 => 9
[6,2]
 => 10000100 => 01000100 => 7
[6,1,1]
 => 100000110 => 100001010 => 9
[5,3]
 => 1001000 => 0010100 => 5
[5,2,1]
 => 10001010 => 11001000 => 13
[9,2]
 => 10000000100 => 01000000100 => ? = 10
[8,2,1]
 => 10000001010 => 11000001000 => ? = 19
[7,2,1,1]
 => 10000010110 => 11000010010 => ? = 18
[6,2,1,1,1]
 => 10000101110 => 11000100110 => ? = 17
[5,2,1,1,1,1]
 => 10001011110 => 11001001110 => ? = 16
[4,2,1,1,1,1,1]
 => 10010111110 => 11010011110 => ? = 15
[3,2,1,1,1,1,1,1]
 => 10101111110 => 11100111110 => ? = 14
[2,2,2,1,1,1,1,1]
 => 1110111110 => 1111011110 => ? = 12
[2,2,1,1,1,1,1,1,1]
 => 11011111110 => 11101111110 => ? = 12
[5,2,2,2,2]
 => 1000111100 => 0100101110 => ? = 9
[3,3,3,1,1,1,1]
 => 1110011110 => 1011101110 => ? = 12
[7,4,2,1]
 => 10001001010 => 11010010000 => ? = 24
[4,4,3,1,1,1]
 => 1101001110 => 1011100110 => ? = 15
[8,4,3]
 => 10000101000 => 00110001000 => ? = 15
[7,5,2,1]
 => 10010001010 => 11001010000 => ? = 23
[7,4,3,1]
 => 10001010010 => 10110010000 => ? = 23
[7,5,3,1]
 => 10010010010 => 10101010000 => ? = 22
[7,4,3,2]
 => 10001010100 => 01110010000 => ? = 22
[6,6,3,1]
 => 1100010010 => 1010011000 => ? = 17
[6,4,3,2,1]
 => 10010101010 => 11110100000 => ? = 29
[6,2,2,2,2,2]
 => 100001111100 => 010001011110 => ? = 11
[7,6,3,1]
 => 10100010010 => 10100110000 => ? = 21
[7,5,4,1]
 => 10010100010 => 10011010000 => ? = 21
[7,5,3,2]
 => 10010010100 => 01101010000 => ? = 21
[6,5,3,2,1]
 => 10100101010 => 11101100000 => ? = 28
[6,5,4,3,1]
 => 10101010010 => 10111100000 => ? = 26
[6,5,4,2,1]
 => 10101001010 => 11011100000 => ? = 27
[7,6,5,2]
 => 10101000100 => 01001110000 => ? = 18
Description
The number of inversions of a binary word.
Matching statistic: St000770
Mapping
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000770: Integer partitions ⟶ ℤResult quality: 57% ●values known / values provided: 57%●distinct values known / distinct values provided: 59%
Values
[1]
 => [1]
 => ? = 1
[2]
 => [1,1]
 => 1
[1,1]
 => [2]
 => 2
[3]
 => [1,1,1]
 => 1
[2,1]
 => [2,1]
 => 4
[1,1,1]
 => [3]
 => 3
[4]
 => [1,1,1,1]
 => 1
[3,1]
 => [2,1,1]
 => 5
[2,2]
 => [2,2]
 => 2
[2,1,1]
 => [3,1]
 => 5
[1,1,1,1]
 => [4]
 => 4
[5]
 => [1,1,1,1,1]
 => 1
[4,1]
 => [2,1,1,1]
 => 6
[3,2]
 => [2,2,1]
 => 4
[3,1,1]
 => [3,1,1]
 => 6
[2,2,1]
 => [3,2]
 => 6
[2,1,1,1]
 => [4,1]
 => 6
[1,1,1,1,1]
 => [5]
 => 5
[6]
 => [1,1,1,1,1,1]
 => 1
[5,1]
 => [2,1,1,1,1]
 => 7
[4,2]
 => [2,2,1,1]
 => 5
[4,1,1]
 => [3,1,1,1]
 => 7
[3,3]
 => [2,2,2]
 => 2
[3,2,1]
 => [3,2,1]
 => 9
[3,1,1,1]
 => [4,1,1]
 => 7
[2,2,2]
 => [3,3]
 => 3
[2,2,1,1]
 => [4,2]
 => 7
[2,1,1,1,1]
 => [5,1]
 => 7
[1,1,1,1,1,1]
 => [6]
 => 6
[7]
 => [1,1,1,1,1,1,1]
 => 1
[6,1]
 => [2,1,1,1,1,1]
 => 8
[5,2]
 => [2,2,1,1,1]
 => 6
[5,1,1]
 => [3,1,1,1,1]
 => 8
[4,3]
 => [2,2,2,1]
 => 4
[4,2,1]
 => [3,2,1,1]
 => 11
[4,1,1,1]
 => [4,1,1,1]
 => 8
[3,3,1]
 => [3,2,2]
 => 7
[3,2,2]
 => [3,3,1]
 => 5
[3,2,1,1]
 => [4,2,1]
 => 10
[3,1,1,1,1]
 => [5,1,1]
 => 8
[2,2,2,1]
 => [4,3]
 => 8
[2,2,1,1,1]
 => [5,2]
 => 8
[2,1,1,1,1,1]
 => [6,1]
 => 8
[1,1,1,1,1,1,1]
 => [7]
 => 7
[8]
 => [1,1,1,1,1,1,1,1]
 => 1
[7,1]
 => [2,1,1,1,1,1,1]
 => 9
[6,2]
 => [2,2,1,1,1,1]
 => 7
[6,1,1]
 => [3,1,1,1,1,1]
 => 9
[5,3]
 => [2,2,2,1,1]
 => 5
[5,2,1]
 => [3,2,1,1,1]
 => 13
[5,1,1,1]
 => [4,1,1,1,1]
 => 9
[9,4]
 => [2,2,2,2,1,1,1,1,1]
 => ? = 8
[8,4,1]
 => [3,2,2,2,1,1,1,1]
 => ? = 17
[7,6]
 => [2,2,2,2,2,2,1]
 => ? = 4
[6,6,1]
 => [3,2,2,2,2,2]
 => ? = 10
[6,5,2]
 => [3,3,2,2,2,1]
 => ? = 11
[6,4,3]
 => [3,3,3,2,1,1]
 => ? = 11
[5,5,3]
 => [3,3,3,2,2]
 => ? = 7
[5,5,2,1]
 => [4,3,2,2,2]
 => ? = 16
[5,4,4]
 => [3,3,3,3,1]
 => ? = 5
[5,4,3,1]
 => [4,3,3,2,1]
 => ? = 17
[5,4,2,2]
 => [4,4,2,2,1]
 => ? = 11
[5,4,2,1,1]
 => [5,3,2,2,1]
 => ? = 19
[5,3,3,2]
 => [4,4,3,1,1]
 => ? = 13
[5,3,3,1,1]
 => [5,3,3,1,1]
 => ? = 15
[5,3,2,2,1]
 => [5,4,2,1,1]
 => ? = 21
[5,2,2,2,2]
 => [5,5,1,1,1]
 => ? = 9
[4,4,4,1]
 => [4,3,3,3]
 => ? = 10
[4,4,3,2]
 => [4,4,3,2]
 => ? = 12
[4,4,3,1,1]
 => [5,3,3,2]
 => ? = 14
[4,4,2,2,1]
 => [5,4,2,2]
 => ? = 16
[4,3,3,3]
 => [4,4,4,1]
 => ? = 6
[4,3,3,2,1]
 => [5,4,3,1]
 => ? = 19
[4,3,2,2,2]
 => [5,5,2,1]
 => ? = 11
[3,3,3,3,1]
 => [5,4,4]
 => ? = 11
[3,3,3,2,2]
 => [5,5,3]
 => ? = 9
[3,3,3,2,1,1]
 => [6,4,3]
 => ? = 16
[3,3,3,1,1,1,1]
 => [7,3,3]
 => ? = 12
[3,3,2,2,2,1]
 => [6,5,2]
 => ? = 16
[3,2,2,2,2,2]
 => [6,6,1]
 => ? = 8
[2,2,2,2,2,2,1]
 => [7,6]
 => ? = 14
[8,5,1]
 => [3,2,2,2,2,1,1,1]
 => ? = 16
[8,4,2]
 => [3,3,2,2,1,1,1,1]
 => ? = 16
[7,7]
 => [2,2,2,2,2,2,2]
 => ? = 2
[7,4,2,1]
 => [4,3,2,2,1,1,1]
 => ? = 24
[6,6,2]
 => [3,3,2,2,2,2]
 => ? = 9
[6,5,3]
 => [3,3,3,2,2,1]
 => ? = 10
[6,4,4]
 => [3,3,3,3,1,1]
 => ? = 6
[5,5,4]
 => [3,3,3,3,2]
 => ? = 6
[5,5,3,1]
 => [4,3,3,2,2]
 => ? = 15
[5,5,2,2]
 => [4,4,2,2,2]
 => ? = 9
[5,4,4,1]
 => [4,3,3,3,1]
 => ? = 13
[5,4,3,2]
 => [4,4,3,2,1]
 => ? = 16
[5,4,3,1,1]
 => [5,3,3,2,1]
 => ? = 18
[5,4,2,2,1]
 => [5,4,2,2,1]
 => ? = 20
[5,3,3,3]
 => [4,4,4,1,1]
 => ? = 7
[5,3,3,2,1]
 => [5,4,3,1,1]
 => ? = 22
[4,4,4,2]
 => [4,4,3,3]
 => ? = 9
[4,4,4,1,1]
 => [5,3,3,3]
 => ? = 11
[4,4,3,3]
 => [4,4,4,2]
 => ? = 7
Description
The major index of an integer partition when read from bottom to top. This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top. For example, the partition $\lambda = (8,6,6,4,3,3)$ has corners at positions 3,6,9, and 13, giving a major index of 31.
Matching statistic: St001232
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 18%
Values
[1]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => 1
[2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[1,1]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[2,1]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => ? = 4
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 5
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 5
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 6
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 4
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 6
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 6
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 6
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => ? = 7
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 5
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 7
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 9
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 7
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 7
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => ? = 7
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => ? = 1
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 8
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => ? = 6
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => ? = 8
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 4
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 11
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 8
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 7
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ? = 5
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 10
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => ? = 8
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 8
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => ? = 8
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => ? = 8
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => ? = 7
[8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => ? = 1
[7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => ? = 9
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => ? = 7
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => ? = 9
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => ? = 5
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => ? = 13
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => ? = 9
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => 2
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 10
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 6
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 12
[4,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => ? = 9
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => ? = 6
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 8
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 11
[3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,1,0,0,1,0,0,0]
 => ? = 11
[3,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
 => ? = 9
[2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 4
[2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => ? = 9
[2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => ? = 9
[2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
 => ? = 9
[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]
 => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => ? = 8
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => 3
[5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => 2
[2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => 5
[4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => 3
[3,3,3,3]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.