Identifier
- St001838: Binary words ⟶ ℤ
Values
0 => 1
1 => 1
00 => 1
01 => 3
10 => 3
11 => 1
000 => 1
001 => 4
010 => 5
011 => 4
100 => 4
101 => 5
110 => 4
111 => 1
0000 => 1
0001 => 5
0010 => 7
0011 => 6
0100 => 7
0101 => 6
0110 => 7
0111 => 5
1000 => 5
1001 => 7
1010 => 6
1011 => 7
1100 => 6
1101 => 7
1110 => 5
1111 => 1
00000 => 1
00001 => 6
00010 => 9
00011 => 8
00100 => 10
00101 => 9
00110 => 10
00111 => 8
01000 => 9
01001 => 10
01010 => 7
01011 => 9
01100 => 10
01101 => 10
01110 => 9
01111 => 6
10000 => 6
10001 => 9
10010 => 10
10011 => 10
10100 => 9
10101 => 7
10110 => 10
10111 => 9
11000 => 8
11001 => 10
11010 => 9
11011 => 10
11100 => 8
11101 => 9
11110 => 6
11111 => 1
000000 => 1
000001 => 7
000010 => 11
000011 => 10
000100 => 13
000101 => 12
000110 => 13
000111 => 11
001000 => 13
001001 => 12
001010 => 11
001011 => 13
001100 => 14
001101 => 14
001110 => 13
001111 => 10
010000 => 11
010001 => 13
010010 => 12
010011 => 14
010100 => 11
010101 => 8
010110 => 13
010111 => 12
011000 => 13
011001 => 14
011010 => 13
011011 => 12
011100 => 13
011101 => 13
011110 => 11
011111 => 7
100000 => 7
100001 => 11
100010 => 13
100011 => 13
100100 => 12
100101 => 13
100110 => 14
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Description
The number of nonempty primitive factors of a binary word.
A word $u$ is a factor of a word $w$ if $w = p u s$ for words $p$ and $s$. A word is primitive, if it is not of the form $u^k$ for a word $u$ and an integer $k\geq 2$.
Apparently, the maximal number of nonempty primitive factors a binary word of length $n$ can have is given by oeis:A131673.
A word $u$ is a factor of a word $w$ if $w = p u s$ for words $p$ and $s$. A word is primitive, if it is not of the form $u^k$ for a word $u$ and an integer $k\geq 2$.
Apparently, the maximal number of nonempty primitive factors a binary word of length $n$ can have is given by oeis:A131673.
Code
def statistic(w):
return sum(1 for f in w.factor_iterator() if f and f.is_primitive())
Created
Sep 16, 2022 at 10:06 by Martin Rubey
Updated
Sep 16, 2022 at 10:06 by Martin Rubey
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