Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000347
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Mapping
St000347: 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 => 0
10 => 1
11 => 0
000 => 0
001 => 0
010 => 1
011 => 0
100 => 3
101 => 1
110 => 3
111 => 0
0000 => 0
0001 => 0
0010 => 1
0011 => 0
0100 => 3
0101 => 1
0110 => 3
0111 => 0
1000 => 6
1001 => 3
1010 => 5
1011 => 1
1100 => 8
1101 => 3
1110 => 6
1111 => 0
00000 => 0
00001 => 0
00010 => 1
00011 => 0
00100 => 3
00101 => 1
00110 => 3
00111 => 0
01000 => 6
01001 => 3
01010 => 5
01011 => 1
01100 => 8
01101 => 3
01110 => 6
01111 => 0
10000 => 10
10001 => 6
10010 => 8
10011 => 3
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 $\pi$.
Matching statistic: St000348
(load all 4 compositions to match this statistic)
Mapping
Mp00104: Binary words —reverse⟶ Binary words
St000348: Binary words ⟶ ℤResult quality: 88% ●values known / values provided: 88%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0
1 => 1 => 0
00 => 00 => 0
01 => 10 => 0
10 => 01 => 1
11 => 11 => 0
000 => 000 => 0
001 => 100 => 0
010 => 010 => 1
011 => 110 => 0
100 => 001 => 3
101 => 101 => 1
110 => 011 => 3
111 => 111 => 0
0000 => 0000 => 0
0001 => 1000 => 0
0010 => 0100 => 1
0011 => 1100 => 0
0100 => 0010 => 3
0101 => 1010 => 1
0110 => 0110 => 3
0111 => 1110 => 0
1000 => 0001 => 6
1001 => 1001 => 3
1010 => 0101 => 5
1011 => 1101 => 1
1100 => 0011 => 8
1101 => 1011 => 3
1110 => 0111 => 6
1111 => 1111 => 0
00000 => 00000 => 0
00001 => 10000 => 0
00010 => 01000 => 1
00011 => 11000 => 0
00100 => 00100 => 3
00101 => 10100 => 1
00110 => 01100 => 3
00111 => 11100 => 0
01000 => 00010 => 6
01001 => 10010 => 3
01010 => 01010 => 5
01011 => 11010 => 1
01100 => 00110 => 8
01101 => 10110 => 3
01110 => 01110 => 6
01111 => 11110 => 0
10000 => 00001 => 10
10001 => 10001 => 6
10010 => 01001 => 8
10011 => 11001 => 3
0000000001 => 1000000000 => ? = 0
0010000001 => 1000000100 => ? = 21
0010101101 => 1011010100 => ? = 18
0010101011 => 1101010100 => ? = 14
0010100111 => 1110010100 => ? = 11
0010011101 => 1011100100 => ? = 15
0010011011 => 1101100100 => ? = 11
0010010111 => 1110100100 => ? = 8
0010001111 => 1111000100 => ? = 6
0001110101 => 1010111000 => ? = 19
0001110011 => 1100111000 => ? = 15
0001101101 => 1011011000 => ? = 15
0001101011 => 1101011000 => ? = 11
0001100111 => 1110011000 => ? = 8
0001011101 => 1011101000 => ? = 12
0001011011 => 1101101000 => ? = 8
0001010111 => 1110101000 => ? = 5
0001001111 => 1111001000 => ? = 3
0000111101 => 1011110000 => ? = 10
0000111011 => 1101110000 => ? = 6
0000110111 => 1110110000 => ? = 3
0000101111 => 1111010000 => ? = 1
0000011111 => 1111100000 => ? = 0
0000000110 => 0110000000 => ? = 3
0000011110 => 0111100000 => ? = 10
0000010010 => 0100100000 => ? = 8
0001100110 => 0110011000 => ? = 22
0001111110 => 0111111000 => ? = 21
0001110010 => 0100111000 => ? = 31
0001001110 => 0111001000 => ? = 15
0001000010 => 0100001000 => ? = 17
0001011010 => 0101101000 => ? = 22
0010101010 => 0101010100 => ? = 30
0010101100 => 0011010100 => ? = 35
0010101110 => 0111010100 => ? = 23
0000000010 => 0100000000 => ? = 1
0000001110 => 0111000000 => ? = 6
0000111110 => 0111110000 => ? = 15
0000001010 => 0101000000 => ? = 5
0000010110 => 0110100000 => ? = 8
0000101110 => 0111010000 => ? = 12
0001011110 => 0111101000 => ? = 17
0001101110 => 0111011000 => ? = 20
0001110110 => 0110111000 => ? = 24
0001111010 => 0101111000 => ? = 29
0001111100 => 0011111000 => ? = 35
0000000101 => 1010000000 => ? = 1
0000001101 => 1011000000 => ? = 3
0000011101 => 1011100000 => ? = 6
0001111101 => 1011111000 => ? = 15
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 $w$.