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Matching statistic: St001371
Mapping
St001371: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1
1 => 0
00 => 2
01 => 2
10 => 0
11 => 0
000 => 3
001 => 3
010 => 3
011 => 2
100 => 0
101 => 0
110 => 0
111 => 0
0000 => 4
0001 => 4
0010 => 4
0011 => 4
0100 => 4
0101 => 4
0110 => 2
0111 => 2
1000 => 0
1001 => 0
1010 => 0
1011 => 0
1100 => 0
1101 => 0
1110 => 0
1111 => 0
00000 => 5
00001 => 5
00010 => 5
00011 => 5
00100 => 5
00101 => 5
00110 => 5
00111 => 4
01000 => 5
01001 => 5
01010 => 5
01011 => 4
01100 => 2
01101 => 2
01110 => 2
01111 => 2
10000 => 0
10001 => 0
10010 => 0
10011 => 0
Description
The length of the longest Yamanouchi prefix of a binary word. This is the largest index $i$ such that in each of the prefixes $w_1$, $w_1w_2$, $w_1w_2\dots w_i$ the number of zeros is greater than or equal to the number of ones.