Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000869
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000869: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => [[2],[]]
 => []
 => 0
1 => [1,1] => [[1,1],[]]
 => []
 => 0
00 => [3] => [[3],[]]
 => []
 => 0
01 => [2,1] => [[2,2],[1]]
 => [1]
 => 1
10 => [1,2] => [[2,1],[]]
 => []
 => 0
11 => [1,1,1] => [[1,1,1],[]]
 => []
 => 0
000 => [4] => [[4],[]]
 => []
 => 0
001 => [3,1] => [[3,3],[2]]
 => [2]
 => 3
010 => [2,2] => [[3,2],[1]]
 => [1]
 => 1
011 => [2,1,1] => [[2,2,2],[1,1]]
 => [1,1]
 => 3
100 => [1,3] => [[3,1],[]]
 => []
 => 0
101 => [1,2,1] => [[2,2,1],[1]]
 => [1]
 => 1
110 => [1,1,2] => [[2,1,1],[]]
 => []
 => 0
111 => [1,1,1,1] => [[1,1,1,1],[]]
 => []
 => 0
0000 => [5] => [[5],[]]
 => []
 => 0
0001 => [4,1] => [[4,4],[3]]
 => [3]
 => 6
0010 => [3,2] => [[4,3],[2]]
 => [2]
 => 3
0011 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 8
0100 => [2,3] => [[4,2],[1]]
 => [1]
 => 1
0101 => [2,2,1] => [[3,3,2],[2,1]]
 => [2,1]
 => 5
0110 => [2,1,2] => [[3,2,2],[1,1]]
 => [1,1]
 => 3
0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 6
1000 => [1,4] => [[4,1],[]]
 => []
 => 0
1001 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 3
1010 => [1,2,2] => [[3,2,1],[1]]
 => [1]
 => 1
1011 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => [1,1]
 => 3
1100 => [1,1,3] => [[3,1,1],[]]
 => []
 => 0
1101 => [1,1,2,1] => [[2,2,1,1],[1]]
 => [1]
 => 1
1110 => [1,1,1,2] => [[2,1,1,1],[]]
 => []
 => 0
1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
 => []
 => 0
00000 => [6] => [[6],[]]
 => []
 => 0
00001 => [5,1] => [[5,5],[4]]
 => [4]
 => 10
00010 => [4,2] => [[5,4],[3]]
 => [3]
 => 6
00011 => [4,1,1] => [[4,4,4],[3,3]]
 => [3,3]
 => 15
00100 => [3,3] => [[5,3],[2]]
 => [2]
 => 3
00101 => [3,2,1] => [[4,4,3],[3,2]]
 => [3,2]
 => 11
00110 => [3,1,2] => [[4,3,3],[2,2]]
 => [2,2]
 => 8
00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => [2,2,2]
 => 15
01000 => [2,4] => [[5,2],[1]]
 => [1]
 => 1
01001 => [2,3,1] => [[4,4,2],[3,1]]
 => [3,1]
 => 8
01010 => [2,2,2] => [[4,3,2],[2,1]]
 => [2,1]
 => 5
01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => 11
01100 => [2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => 3
01101 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => 8
01110 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => 6
01111 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => 10
10000 => [1,5] => [[5,1],[]]
 => []
 => 0
10001 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 6
10010 => [1,3,2] => [[4,3,1],[2]]
 => [2]
 => 3
10011 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => [2,2]
 => 8
Description
The sum of the hook lengths of an integer partition. For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the sum of all hook lengths of a partition.
Matching statistic: St000348
(load all 4 compositions to match this statistic)
Mapping
St000348: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 0
01 => 1
10 => 0
11 => 0
000 => 0
001 => 3
010 => 1
011 => 3
100 => 0
101 => 1
110 => 0
111 => 0
0000 => 0
0001 => 6
0010 => 3
0011 => 8
0100 => 1
0101 => 5
0110 => 3
0111 => 6
1000 => 0
1001 => 3
1010 => 1
1011 => 3
1100 => 0
1101 => 1
1110 => 0
1111 => 0
00000 => 0
00001 => 10
00010 => 6
00011 => 15
00100 => 3
00101 => 11
00110 => 8
00111 => 15
01000 => 1
01001 => 8
01010 => 5
01011 => 11
01100 => 3
01101 => 8
01110 => 6
01111 => 10
10000 => 0
10001 => 6
10010 => 3
10011 => 8
=> ? = 0
Description
The non-inversion sum of a binary word. A pair $a < b$ is an noninversion of a binary word $w = w_1 \cdots w_n$ if $w_a < w_b$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $w$.
Matching statistic: St000347
(load all 4 compositions to match this statistic)
Mapping
Mp00104: Binary words —reverse⟶ Binary words
St000347: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0
1 => 1 => 0
00 => 00 => 0
01 => 10 => 1
10 => 01 => 0
11 => 11 => 0
000 => 000 => 0
001 => 100 => 3
010 => 010 => 1
011 => 110 => 3
100 => 001 => 0
101 => 101 => 1
110 => 011 => 0
111 => 111 => 0
0000 => 0000 => 0
0001 => 1000 => 6
0010 => 0100 => 3
0011 => 1100 => 8
0100 => 0010 => 1
0101 => 1010 => 5
0110 => 0110 => 3
0111 => 1110 => 6
1000 => 0001 => 0
1001 => 1001 => 3
1010 => 0101 => 1
1011 => 1101 => 3
1100 => 0011 => 0
1101 => 1011 => 1
1110 => 0111 => 0
1111 => 1111 => 0
00000 => 00000 => 0
00001 => 10000 => 10
00010 => 01000 => 6
00011 => 11000 => 15
00100 => 00100 => 3
00101 => 10100 => 11
00110 => 01100 => 8
00111 => 11100 => 15
01000 => 00010 => 1
01001 => 10010 => 8
01010 => 01010 => 5
01011 => 11010 => 11
01100 => 00110 => 3
01101 => 10110 => 8
01110 => 01110 => 6
01111 => 11110 => 10
10000 => 00001 => 0
10001 => 10001 => 6
10010 => 01001 => 3
10011 => 11001 => 8
=> => ? = 0
Description
The inversion sum of a binary word. A pair $a < b$ is an inversion of a binary word $w = w_1 \cdots w_n$ if $w_a = 1 > 0 = w_b$. The inversion sum is given by $\sum(b-a)$ over all inversions of $\pi$.