Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000393
(load all 14 compositions to match this statistic)
Mapping
St000393: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1
1 => 1
00 => 2
01 => 1
10 => 2
11 => 2
000 => 3
001 => 2
010 => 2
011 => 2
100 => 3
101 => 2
110 => 3
111 => 3
0000 => 4
0001 => 3
0010 => 3
0011 => 3
0100 => 3
0101 => 2
0110 => 3
0111 => 3
1000 => 4
1001 => 3
1010 => 3
1011 => 3
1100 => 4
1101 => 3
1110 => 4
1111 => 4
00000 => 5
00001 => 4
00010 => 4
00011 => 4
00100 => 4
00101 => 3
00110 => 4
00111 => 4
01000 => 4
01001 => 3
01010 => 3
01011 => 3
01100 => 4
01101 => 3
01110 => 4
01111 => 4
10000 => 5
10001 => 4
10010 => 4
10011 => 4
Description
The number of strictly increasing runs in a binary word.
Matching statistic: St000863
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
St000863: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 60%
Values
0 => [2] => [1,1,0,0]
 => [1,2] => 2 = 1 + 1
1 => [1,1] => [1,0,1,0]
 => [2,1] => 2 = 1 + 1
00 => [3] => [1,1,1,0,0,0]
 => [1,2,3] => 3 = 2 + 1
01 => [2,1] => [1,1,0,0,1,0]
 => [1,3,2] => 2 = 1 + 1
10 => [1,2] => [1,0,1,1,0,0]
 => [2,1,3] => 3 = 2 + 1
11 => [1,1,1] => [1,0,1,0,1,0]
 => [2,3,1] => 3 = 2 + 1
000 => [4] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 4 = 3 + 1
001 => [3,1] => [1,1,1,0,0,0,1,0]
 => [1,2,4,3] => 3 = 2 + 1
010 => [2,2] => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 3 = 2 + 1
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => [1,3,4,2] => 3 = 2 + 1
100 => [1,3] => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 4 = 3 + 1
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => [2,1,4,3] => 3 = 2 + 1
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => [2,3,1,4] => 4 = 3 + 1
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => [2,3,4,1] => 4 = 3 + 1
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 5 = 4 + 1
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => [1,2,3,5,4] => 4 = 3 + 1
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => [1,2,4,3,5] => 4 = 3 + 1
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => [1,2,4,5,3] => 4 = 3 + 1
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,4,5] => 4 = 3 + 1
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4] => 3 = 2 + 1
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => [1,3,4,2,5] => 4 = 3 + 1
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => [1,3,4,5,2] => 4 = 3 + 1
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => 5 = 4 + 1
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,5,4] => 4 = 3 + 1
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,5] => 4 = 3 + 1
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,5,3] => 4 = 3 + 1
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => [2,3,1,4,5] => 5 = 4 + 1
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => [2,3,1,5,4] => 4 = 3 + 1
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => [2,3,4,1,5] => 5 = 4 + 1
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,1] => 5 = 4 + 1
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => 6 = 5 + 1
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,2,3,4,6,5] => 5 = 4 + 1
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,2,3,5,4,6] => 5 = 4 + 1
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,2,3,5,6,4] => 5 = 4 + 1
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,2,4,3,5,6] => 5 = 4 + 1
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,2,4,3,6,5] => 4 = 3 + 1
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,2,4,5,3,6] => 5 = 4 + 1
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => [1,2,4,5,6,3] => 5 = 4 + 1
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,3,2,4,5,6] => 5 = 4 + 1
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,3,2,4,6,5] => 4 = 3 + 1
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4,6] => 4 = 3 + 1
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,3,2,5,6,4] => 4 = 3 + 1
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,3,4,2,5,6] => 5 = 4 + 1
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,3,4,2,6,5] => 4 = 3 + 1
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,3,4,5,2,6] => 5 = 4 + 1
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,3,4,5,6,2] => 5 = 4 + 1
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,3,4,5,6] => 6 = 5 + 1
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [2,1,3,4,6,5] => 5 = 4 + 1
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [2,1,3,5,4,6] => 5 = 4 + 1
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [2,1,3,5,6,4] => 5 = 4 + 1
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [2,1,3,4,5,6,7] => ? = 6 + 1
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => [2,1,3,4,5,7,6] => ? = 5 + 1
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [2,1,3,4,6,5,7] => ? = 5 + 1
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => [2,1,3,4,6,7,5] => ? = 5 + 1
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [2,1,3,5,4,6,7] => ? = 5 + 1
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [2,1,3,5,4,7,6] => ? = 4 + 1
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => [2,1,3,5,6,4,7] => ? = 5 + 1
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [2,1,3,5,6,7,4] => ? = 5 + 1
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,4,3,5,6,7] => ? = 5 + 1
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,1,4,3,5,7,6] => ? = 4 + 1
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,6,5,7] => ? = 4 + 1
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,6,7,5] => ? = 4 + 1
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,4,5,3,6,7] => ? = 5 + 1
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,4,5,3,7,6] => ? = 4 + 1
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,4,5,6,3,7] => ? = 5 + 1
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,4,5,6,7,3] => ? = 5 + 1
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,1,4,5,6,7] => ? = 6 + 1
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [2,3,1,4,5,7,6] => ? = 5 + 1
110010 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [2,3,1,4,6,5,7] => ? = 5 + 1
110011 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [2,3,1,4,6,7,5] => ? = 5 + 1
110100 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [2,3,1,5,4,6,7] => ? = 5 + 1
110101 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [2,3,1,5,4,7,6] => ? = 4 + 1
110110 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [2,3,1,5,6,4,7] => ? = 5 + 1
110111 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [2,3,1,5,6,7,4] => ? = 5 + 1
111000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,1,5,6,7] => ? = 6 + 1
111001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [2,3,4,1,5,7,6] => ? = 5 + 1
111010 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [2,3,4,1,6,5,7] => ? = 5 + 1
111011 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [2,3,4,1,6,7,5] => ? = 5 + 1
111100 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [2,3,4,5,1,6,7] => ? = 6 + 1
111101 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [2,3,4,5,1,7,6] => ? = 5 + 1
111110 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [2,3,4,5,6,1,7] => ? = 6 + 1
111111 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,6,7,1] => ? = 6 + 1
0000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [1,2,3,4,5,6,7,8] => ? = 7 + 1
0000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,2,3,4,5,6,8,7] => ? = 6 + 1
0000010 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,2,3,4,5,7,6,8] => ? = 6 + 1
0000011 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
 => [1,2,3,4,5,7,8,6] => ? = 6 + 1
0000100 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
 => [1,2,3,4,6,5,7,8] => ? = 6 + 1
0000101 => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
 => [1,2,3,4,6,5,8,7] => ? = 5 + 1
0000110 => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
 => [1,2,3,4,6,7,5,8] => ? = 6 + 1
0000111 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
 => [1,2,3,4,6,7,8,5] => ? = 6 + 1
0001000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,2,3,5,4,6,7,8] => ? = 6 + 1
0001001 => [4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
 => [1,2,3,5,4,6,8,7] => ? = 5 + 1
0001010 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
 => [1,2,3,5,4,7,6,8] => ? = 5 + 1
0001011 => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
 => [1,2,3,5,4,7,8,6] => ? = 5 + 1
0001100 => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
 => [1,2,3,5,6,4,7,8] => ? = 6 + 1
0001101 => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,6,4,8,7] => ? = 5 + 1
0001110 => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,6,7,4,8] => ? = 6 + 1
0001111 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => [1,2,3,5,6,7,8,4] => ? = 6 + 1
0010000 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
 => [1,2,4,3,5,6,7,8] => ? = 6 + 1
0010001 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,2,4,3,5,6,8,7] => ? = 5 + 1
Description
The length of the first row of the shifted shape of a permutation. The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing. The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled. This statistic records the length of the first row of $P$ and $Q$.
Matching statistic: St001237
(load all 8 compositions to match this statistic)
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001237: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 50%
Values
0 => [2] => [1,1,0,0]
 => 3 = 1 + 2
1 => [1,1] => [1,0,1,0]
 => 3 = 1 + 2
00 => [3] => [1,1,1,0,0,0]
 => 4 = 2 + 2
01 => [2,1] => [1,1,0,0,1,0]
 => 3 = 1 + 2
10 => [1,2] => [1,0,1,1,0,0]
 => 4 = 2 + 2
11 => [1,1,1] => [1,0,1,0,1,0]
 => 4 = 2 + 2
000 => [4] => [1,1,1,1,0,0,0,0]
 => 5 = 3 + 2
001 => [3,1] => [1,1,1,0,0,0,1,0]
 => 4 = 2 + 2
010 => [2,2] => [1,1,0,0,1,1,0,0]
 => 4 = 2 + 2
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
 => 4 = 2 + 2
100 => [1,3] => [1,0,1,1,1,0,0,0]
 => 5 = 3 + 2
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
 => 4 = 2 + 2
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
 => 5 = 3 + 2
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
 => 5 = 3 + 2
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 6 = 4 + 2
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 5 = 3 + 2
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
 => 5 = 3 + 2
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 5 = 3 + 2
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
 => 5 = 3 + 2
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
 => 4 = 2 + 2
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 5 = 3 + 2
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
 => 5 = 3 + 2
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
 => 6 = 4 + 2
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
 => 5 = 3 + 2
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
 => 5 = 3 + 2
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
 => 5 = 3 + 2
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
 => 6 = 4 + 2
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
 => 5 = 3 + 2
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
 => 6 = 4 + 2
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
 => 6 = 4 + 2
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 7 = 5 + 2
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 6 = 4 + 2
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 6 = 4 + 2
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
 => 6 = 4 + 2
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 6 = 4 + 2
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 5 = 3 + 2
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
 => 6 = 4 + 2
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 6 = 4 + 2
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 6 = 4 + 2
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 5 = 3 + 2
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 5 = 3 + 2
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 5 = 3 + 2
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => 6 = 4 + 2
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => 5 = 3 + 2
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => 6 = 4 + 2
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 6 = 4 + 2
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
 => 7 = 5 + 2
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 6 = 4 + 2
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 6 = 4 + 2
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => 6 = 4 + 2
000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 6 + 2
000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 5 + 2
000010 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 5 + 2
000011 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 5 + 2
000100 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 5 + 2
000101 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
 => ? = 4 + 2
000110 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0]
 => ? = 5 + 2
000111 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 5 + 2
001000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 5 + 2
001001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 + 2
001010 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
 => ? = 4 + 2
001011 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => ? = 4 + 2
001100 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0]
 => ? = 5 + 2
001101 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]
 => ? = 4 + 2
001110 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]
 => ? = 5 + 2
001111 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 5 + 2
010000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 5 + 2
010001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 4 + 2
010010 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
 => ? = 4 + 2
010011 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 4 + 2
010100 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
 => ? = 4 + 2
010101 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => ? = 3 + 2
010110 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => ? = 4 + 2
010111 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 4 + 2
011000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => ? = 5 + 2
011001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]
 => ? = 4 + 2
011010 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0]
 => ? = 4 + 2
011011 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 4 + 2
011100 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
 => ? = 5 + 2
011101 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 4 + 2
011110 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 5 + 2
011111 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 5 + 2
100000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => ? = 6 + 2
100001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
 => ? = 5 + 2
100010 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => ? = 5 + 2
100011 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 5 + 2
100100 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => ? = 5 + 2
100101 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => ? = 4 + 2
100110 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => ? = 5 + 2
100111 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 5 + 2
101000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => ? = 5 + 2
101001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => ? = 4 + 2
101010 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => ? = 4 + 2
101011 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 4 + 2
101100 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => ? = 5 + 2
101101 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => ? = 4 + 2
101110 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => ? = 5 + 2
101111 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 5 + 2
110000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => ? = 6 + 2
110001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => ? = 5 + 2
Description
The number of simple modules with injective dimension at most one or dominant dimension at least one.