Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000142
Mapping
Mp00105: Binary words —complement⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000142: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => [1,1] => [1,1]
 => 0
1 => 0 => [2] => [2]
 => 1
00 => 11 => [1,1,1] => [1,1,1]
 => 0
01 => 10 => [1,2] => [2,1]
 => 1
10 => 01 => [2,1] => [2,1]
 => 1
11 => 00 => [3] => [3]
 => 0
000 => 111 => [1,1,1,1] => [1,1,1,1]
 => 0
001 => 110 => [1,1,2] => [2,1,1]
 => 1
010 => 101 => [1,2,1] => [2,1,1]
 => 1
011 => 100 => [1,3] => [3,1]
 => 0
100 => 011 => [2,1,1] => [2,1,1]
 => 1
101 => 010 => [2,2] => [2,2]
 => 2
110 => 001 => [3,1] => [3,1]
 => 0
111 => 000 => [4] => [4]
 => 1
0000 => 1111 => [1,1,1,1,1] => [1,1,1,1,1]
 => 0
0001 => 1110 => [1,1,1,2] => [2,1,1,1]
 => 1
0010 => 1101 => [1,1,2,1] => [2,1,1,1]
 => 1
0011 => 1100 => [1,1,3] => [3,1,1]
 => 0
0100 => 1011 => [1,2,1,1] => [2,1,1,1]
 => 1
0101 => 1010 => [1,2,2] => [2,2,1]
 => 2
0110 => 1001 => [1,3,1] => [3,1,1]
 => 0
0111 => 1000 => [1,4] => [4,1]
 => 1
1000 => 0111 => [2,1,1,1] => [2,1,1,1]
 => 1
1001 => 0110 => [2,1,2] => [2,2,1]
 => 2
1010 => 0101 => [2,2,1] => [2,2,1]
 => 2
1011 => 0100 => [2,3] => [3,2]
 => 1
1100 => 0011 => [3,1,1] => [3,1,1]
 => 0
1101 => 0010 => [3,2] => [3,2]
 => 1
1110 => 0001 => [4,1] => [4,1]
 => 1
1111 => 0000 => [5] => [5]
 => 0
00000 => 11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1]
 => 0
00001 => 11110 => [1,1,1,1,2] => [2,1,1,1,1]
 => 1
00010 => 11101 => [1,1,1,2,1] => [2,1,1,1,1]
 => 1
00011 => 11100 => [1,1,1,3] => [3,1,1,1]
 => 0
00100 => 11011 => [1,1,2,1,1] => [2,1,1,1,1]
 => 1
00101 => 11010 => [1,1,2,2] => [2,2,1,1]
 => 2
00110 => 11001 => [1,1,3,1] => [3,1,1,1]
 => 0
00111 => 11000 => [1,1,4] => [4,1,1]
 => 1
01000 => 10111 => [1,2,1,1,1] => [2,1,1,1,1]
 => 1
01001 => 10110 => [1,2,1,2] => [2,2,1,1]
 => 2
01010 => 10101 => [1,2,2,1] => [2,2,1,1]
 => 2
01011 => 10100 => [1,2,3] => [3,2,1]
 => 1
01100 => 10011 => [1,3,1,1] => [3,1,1,1]
 => 0
01101 => 10010 => [1,3,2] => [3,2,1]
 => 1
01110 => 10001 => [1,4,1] => [4,1,1]
 => 1
01111 => 10000 => [1,5] => [5,1]
 => 0
10000 => 01111 => [2,1,1,1,1] => [2,1,1,1,1]
 => 1
10001 => 01110 => [2,1,1,2] => [2,2,1,1]
 => 2
10010 => 01101 => [2,1,2,1] => [2,2,1,1]
 => 2
10011 => 01100 => [2,1,3] => [3,2,1]
 => 1
Description
The number of even parts of a partition.
Matching statistic: St000389
(load all 2 compositions to match this statistic)
Mapping
St000389: Binary words ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 1
00 => 0
01 => 1
10 => 1
11 => 0
000 => 0
001 => 1
010 => 1
011 => 0
100 => 1
101 => 2
110 => 0
111 => 1
0000 => 0
0001 => 1
0010 => 1
0011 => 0
0100 => 1
0101 => 2
0110 => 0
0111 => 1
1000 => 1
1001 => 2
1010 => 2
1011 => 1
1100 => 0
1101 => 1
1110 => 1
1111 => 0
00000 => 0
00001 => 1
00010 => 1
00011 => 0
00100 => 1
00101 => 2
00110 => 0
00111 => 1
01000 => 1
01001 => 2
01010 => 2
01011 => 1
01100 => 0
01101 => 1
01110 => 1
01111 => 0
10000 => 1
10001 => 2
10010 => 2
10011 => 1
1111111111 => ? = 0
1010000001 => ? = 3
1000000101 => ? = 3
10111011110 => ? = 2
10111101110 => ? = 2
10001000000 => ? = 2
11101011110 => ? = 2
11011101110 => ? = 2
10101010110 => ? = 4
11101101110 => ? = 2
10100000000 => ? = 2
10101011010 => ? = 4
11101110110 => ? = 2
=> ? = 0
11010101010 => ? = 4
11010101100 => ? = 2
11011010100 => ? = 2
0110000110 => ? = 0
0110011000 => ? = 0
0110011110 => ? = 0
0111100110 => ? = 0
0111111110 => ? = 0
000000000000 => ? = 0
00101011011 => ? = 2
00101101011 => ? = 2
00110101011 => ? = 2
01010101011 => ? = 4
00000000000 => ? = 0
01111111110 => ? = 1
00100000001 => ? = 2
10000000001 => ? = 2
11111111111 => ? = 1
01011110111 => ? = 2
01101010101 => ? = 4
01110111101 => ? = 2
01111011101 => ? = 2
01111010111 => ? = 2
10110101010 => ? = 4
10111011101 => ? = 4
10111110111 => ? = 3
10101101010 => ? = 4
10101110111 => ? = 4
10111010111 => ? = 4
10111101111 => ? = 1
11011101101 => ? = 2
11011011101 => ? = 2
11011011011 => ? = 0
11011101011 => ? = 2
11011110111 => ? = 1
11010111011 => ? = 2
Description
The number of runs of ones of odd length in a binary word.