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Matching statistic: St001267
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Mapping
St001267: 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 => 1
010 => 2
011 => 1
100 => 3
101 => 2
110 => 3
111 => 3
0000 => 4
0001 => 1
0010 => 2
0011 => 1
0100 => 3
0101 => 2
0110 => 2
0111 => 1
1000 => 4
1001 => 2
1010 => 3
1011 => 2
1100 => 4
1101 => 3
1110 => 4
1111 => 4
00000 => 5
00001 => 1
00010 => 2
00011 => 1
00100 => 3
00101 => 1
00110 => 2
00111 => 1
01000 => 4
01001 => 2
01010 => 3
01011 => 1
01100 => 3
01101 => 2
01110 => 2
01111 => 1
10000 => 5
10001 => 2
10010 => 3
10011 => 2
Description
The length of the Lyndon factorization of the binary word. The Lyndon factorization of a finite word w is its unique factorization as a non-increasing product of Lyndon words, i.e., $w = l_1\dots l_n$ where each $l_i$ is a Lyndon word and $l_1 \geq\dots\geq l_n$.