Identifier
- St000543: Binary words ⟶ ℤ
Values
0 => 1
1 => 1
00 => 1
01 => 2
10 => 2
11 => 1
000 => 1
001 => 3
010 => 3
011 => 3
100 => 3
101 => 3
110 => 3
111 => 1
0000 => 1
0001 => 4
0010 => 4
0011 => 4
0100 => 4
0101 => 2
0110 => 4
0111 => 4
1000 => 4
1001 => 4
1010 => 2
1011 => 4
1100 => 4
1101 => 4
1110 => 4
1111 => 1
00000 => 1
00001 => 5
00010 => 5
00011 => 5
00100 => 5
00101 => 5
00110 => 5
00111 => 5
01000 => 5
01001 => 5
01010 => 5
01011 => 5
01100 => 5
01101 => 5
01110 => 5
01111 => 5
10000 => 5
10001 => 5
10010 => 5
10011 => 5
10100 => 5
10101 => 5
10110 => 5
10111 => 5
11000 => 5
11001 => 5
11010 => 5
11011 => 5
11100 => 5
11101 => 5
11110 => 5
11111 => 1
000000 => 1
000001 => 6
000010 => 6
000011 => 6
000100 => 6
000101 => 6
000110 => 6
000111 => 6
001000 => 6
001001 => 3
001010 => 6
001011 => 6
001100 => 6
001101 => 6
001110 => 6
001111 => 6
010000 => 6
010001 => 6
010010 => 3
010011 => 6
010100 => 6
010101 => 2
010110 => 6
010111 => 6
011000 => 6
011001 => 6
011010 => 6
011011 => 3
011100 => 6
011101 => 6
011110 => 6
011111 => 6
100000 => 6
100001 => 6
100010 => 6
100011 => 6
100100 => 3
100101 => 6
100110 => 6
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Description
The size of the conjugacy class of a binary word.
Two words $u$ and $v$ are conjugate, if $u=w_1 w_2$ and $v=w_2 w_1$, see Section 1.3 of [1].
Two words $u$ and $v$ are conjugate, if $u=w_1 w_2$ and $v=w_2 w_1$, see Section 1.3 of [1].
References
[1] Lothaire, M. Combinatorics on words MathSciNet:0675953
Code
def statistic(w):
return len(w.conjugates())
Created
Jun 29, 2016 at 06:43 by Martin Rubey
Updated
Jun 29, 2016 at 07:56 by Martin Rubey
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