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
100111=>6
101000=>6
101001=>6
101010=>2
101011=>6
101100=>6
101101=>3
101110=>6
101111=>6
110000=>6
110001=>6
110010=>6
110011=>6
110100=>6
110101=>6
110110=>3
110111=>6
111000=>6
111001=>6
111010=>6
111011=>6
111100=>6
111101=>6
111110=>6
111111=>1
0000000=>1
0000001=>7
0000010=>7
0000011=>7
0000100=>7
0000101=>7
0000110=>7
0000111=>7
0001000=>7
0001001=>7
0001010=>7
0001011=>7
0001100=>7
0001101=>7
0001110=>7
0001111=>7
0010000=>7
0010001=>7
0010010=>7
0010011=>7
0010100=>7
0010101=>7
0010110=>7
0010111=>7
0011000=>7
0011001=>7
0011010=>7
0011011=>7
0011100=>7
0011101=>7
0011110=>7
0011111=>7
0100000=>7
0100001=>7
0100010=>7
0100011=>7
0100100=>7
0100101=>7
0100110=>7
0100111=>7
0101000=>7
0101001=>7
0101010=>7
0101011=>7
0101100=>7
0101101=>7
0101110=>7
0101111=>7
0110000=>7
0110001=>7
0110010=>7
0110011=>7
0110100=>7
0110101=>7
0110110=>7
0110111=>7
0111000=>7
0111001=>7
0111010=>7
0111011=>7
0111100=>7
0111101=>7
0111110=>7
0111111=>7
1000000=>7
1000001=>7
1000010=>7
1000011=>7
1000100=>7
1000101=>7
1000110=>7
1000111=>7
1001000=>7
1001001=>7
1001010=>7
1001011=>7
1001100=>7
1001101=>7
1001110=>7
1001111=>7
1010000=>7
1010001=>7
1010010=>7
1010011=>7
1010100=>7
1010101=>7
1010110=>7
1010111=>7
1011000=>7
1011001=>7
1011010=>7
1011011=>7
1011100=>7
1011101=>7
1011110=>7
1011111=>7
1100000=>7
1100001=>7
1100010=>7
1100011=>7
1100100=>7
1100101=>7
1100110=>7
1100111=>7
1101000=>7
1101001=>7
1101010=>7
1101011=>7
1101100=>7
1101101=>7
1101110=>7
1101111=>7
1110000=>7
1110001=>7
1110010=>7
1110011=>7
1110100=>7
1110101=>7
1110110=>7
1110111=>7
1111000=>7
1111001=>7
1111010=>7
1111011=>7
1111100=>7
1111101=>7
1111110=>7
1111111=>1
00000000=>1
00000001=>8
00000010=>8
00000011=>8
00000100=>8
00000101=>8
00000110=>8
00000111=>8
00001000=>8
00001001=>8
00001010=>8
00001011=>8
00001100=>8
00001101=>8
00001110=>8
00001111=>8
00010000=>8
00010001=>4
00010010=>8
00010011=>8
00010100=>8
00010101=>8
00010110=>8
00010111=>8
00011000=>8
00011001=>8
00011010=>8
00011011=>8
00011100=>8
00011101=>8
00011110=>8
00011111=>8
00100000=>8
00100001=>8
00100010=>4
00100011=>8
00100100=>8
00100101=>8
00100110=>8
00100111=>8
00101000=>8
00101001=>8
00101010=>8
00101011=>8
00101100=>8
00101101=>8
00101110=>8
00101111=>8
00110000=>8
00110001=>8
00110010=>8
00110011=>4
00110100=>8
00110101=>8
00110110=>8
00110111=>8
00111000=>8
00111001=>8
00111010=>8
00111011=>8
00111100=>8
00111101=>8
00111110=>8
00111111=>8
01000000=>8
01000001=>8
01000010=>8
01000011=>8
01000100=>4
01000101=>8
01000110=>8
01000111=>8
01001000=>8
01001001=>8
01001010=>8
01001011=>8
01001100=>8
01001101=>8
01001110=>8
01001111=>8
01010000=>8
01010001=>8
01010010=>8
01010011=>8
01010100=>8
01010101=>2
01010110=>8
01010111=>8
01011000=>8
01011001=>8
01011010=>8
01011011=>8
01011100=>8
01011101=>8
01011110=>8
01011111=>8
01100000=>8
01100001=>8
01100010=>8
01100011=>8
01100100=>8
01100101=>8
01100110=>4
01100111=>8
01101000=>8
01101001=>8
01101010=>8
01101011=>8
01101100=>8
01101101=>8
01101110=>8
01101111=>8
01110000=>8
01110001=>8
01110010=>8
01110011=>8
01110100=>8
01110101=>8
01110110=>8
01110111=>4
01111000=>8
01111001=>8
01111010=>8
01111011=>8
01111100=>8
01111101=>8
01111110=>8
01111111=>8
10000000=>8
10000001=>8
10000010=>8
10000011=>8
10000100=>8
10000101=>8
10000110=>8
10000111=>8
10001000=>4
10001001=>8
10001010=>8
10001011=>8
10001100=>8
10001101=>8
10001110=>8
10001111=>8
10010000=>8
10010001=>8
10010010=>8
10010011=>8
10010100=>8
10010101=>8
10010110=>8
10010111=>8
10011000=>8
10011001=>4
10011010=>8
10011011=>8
10011100=>8
10011101=>8
10011110=>8
10011111=>8
10100000=>8
10100001=>8
10100010=>8
10100011=>8
10100100=>8
10100101=>8
10100110=>8
10100111=>8
10101000=>8
10101001=>8
10101010=>2
10101011=>8
10101100=>8
10101101=>8
10101110=>8
10101111=>8
10110000=>8
10110001=>8
10110010=>8
10110011=>8
10110100=>8
10110101=>8
10110110=>8
10110111=>8
10111000=>8
10111001=>8
10111010=>8
10111011=>4
10111100=>8
10111101=>8
10111110=>8
10111111=>8
11000000=>8
11000001=>8
11000010=>8
11000011=>8
11000100=>8
11000101=>8
11000110=>8
11000111=>8
11001000=>8
11001001=>8
11001010=>8
11001011=>8
11001100=>4
11001101=>8
11001110=>8
11001111=>8
11010000=>8
11010001=>8
11010010=>8
11010011=>8
11010100=>8
11010101=>8
11010110=>8
11010111=>8
11011000=>8
11011001=>8
11011010=>8
11011011=>8
11011100=>8
11011101=>4
11011110=>8
11011111=>8
11100000=>8
11100001=>8
11100010=>8
11100011=>8
11100100=>8
11100101=>8
11100110=>8
11100111=>8
11101000=>8
11101001=>8
11101010=>8
11101011=>8
11101100=>8
11101101=>8
11101110=>4
11101111=>8
11110000=>8
11110001=>8
11110010=>8
11110011=>8
11110100=>8
11110101=>8
11110110=>8
11110111=>8
11111000=>8
11111001=>8
11111010=>8
11111011=>8
11111100=>8
11111101=>8
11111110=>8
11111111=>1
000000000=>1
000000001=>9
000000010=>9
000000011=>9
000000100=>9
000000101=>9
000000110=>9
000000111=>9
000001000=>9
000001001=>9
000001010=>9
000001011=>9
000001100=>9
000001101=>9
000001110=>9
000001111=>9
000010000=>9
000010001=>9
000010010=>9
000010011=>9
000010100=>9
000010101=>9
000010110=>9
000010111=>9
000011000=>9
000011001=>9
000011010=>9
000011011=>9
000011100=>9
000011101=>9
000011110=>9
000011111=>9
000100000=>9
000100001=>9
000100010=>9
000100011=>9
000100100=>9
000100101=>9
000100110=>9
000100111=>9
000101000=>9
000101001=>9
000101010=>9
000101011=>9
000101100=>9
000101101=>9
000101110=>9
000101111=>9
000110000=>9
000110001=>9
000110010=>9
000110011=>9
000110100=>9
000110101=>9
000110110=>9
000110111=>9
000111000=>9
000111001=>9
000111010=>9
000111011=>9
000111100=>9
000111101=>9
000111110=>9
000111111=>9
001000000=>9
001000001=>9
001000010=>9
001000011=>9
001000100=>9
001000101=>9
001000110=>9
001000111=>9
001001000=>9
001001001=>3
001001010=>9
001001011=>9
001001100=>9
001001101=>9
001001110=>9
001001111=>9
001010000=>9
001010001=>9
001010010=>9
001010011=>9
001010100=>9
001010101=>9
001010110=>9
001010111=>9
001011000=>9
001011001=>9
001011010=>9
001011011=>9
001011100=>9
001011101=>9
001011110=>9
001011111=>9
001100000=>9
001100001=>9
001100010=>9
001100011=>9
001100100=>9
001100101=>9
001100110=>9
001100111=>9
001101000=>9
001101001=>9
001101010=>9
001101011=>9
001101100=>9
001101101=>9
001101110=>9
001101111=>9
001110000=>9
001110001=>9
001110010=>9
001110011=>9
001110100=>9
001110101=>9
001110110=>9
001110111=>9
001111000=>9
001111001=>9
001111010=>9
001111011=>9
001111100=>9
001111101=>9
001111110=>9
001111111=>9
010000000=>9
010000001=>9
010000010=>9
010000011=>9
010000100=>9
010000101=>9
010000110=>9
010000111=>9
010001000=>9
010001001=>9
010001010=>9
010001011=>9
010001100=>9
010001101=>9
010001110=>9
010001111=>9
010010000=>9
010010001=>9
010010010=>3
010010011=>9
010010100=>9
010010101=>9
010010110=>9
010010111=>9
010011000=>9
010011001=>9
010011010=>9
010011011=>9
010011100=>9
010011101=>9
010011110=>9
010011111=>9
010100000=>9
010100001=>9
010100010=>9
010100011=>9
010100100=>9
010100101=>9
010100110=>9
010100111=>9
010101000=>9
010101001=>9
010101010=>9
010101011=>9
010101100=>9
010101101=>9
010101110=>9
010101111=>9
010110000=>9
010110001=>9
010110010=>9
010110011=>9
010110100=>9
010110101=>9
010110110=>9
010110111=>9
010111000=>9
010111001=>9
010111010=>9
010111011=>9
010111100=>9
010111101=>9
010111110=>9
010111111=>9
011000000=>9
011000001=>9
011000010=>9
011000011=>9
011000100=>9
011000101=>9
011000110=>9
011000111=>9
011001000=>9
011001001=>9
011001010=>9
011001011=>9
011001100=>9
011001101=>9
011001110=>9
011001111=>9
011010000=>9
011010001=>9
011010010=>9
011010011=>9
011010100=>9
011010101=>9
011010110=>9
011010111=>9
011011000=>9
011011001=>9
011011010=>9
011011011=>3
011011100=>9
011011101=>9
011011110=>9
011011111=>9
011100000=>9
011100001=>9
011100010=>9
011100011=>9
011100100=>9
011100101=>9
011100110=>9
011100111=>9
011101000=>9
011101001=>9
011101010=>9
011101011=>9
011101100=>9
011101101=>9
011101110=>9
011101111=>9
011110000=>9
011110001=>9
011110010=>9
011110011=>9
011110100=>9
011110101=>9
011110110=>9
011110111=>9
011111000=>9
011111001=>9
011111010=>9
011111011=>9
011111100=>9
011111101=>9
011111110=>9
011111111=>9
100000000=>9
100000001=>9
100000010=>9
100000011=>9
100000100=>9
100000101=>9
100000110=>9
100000111=>9
100001000=>9
100001001=>9
100001010=>9
100001011=>9
100001100=>9
100001101=>9
100001110=>9
100001111=>9
100010000=>9
100010001=>9
100010010=>9
100010011=>9
100010100=>9
100010101=>9
100010110=>9
100010111=>9
100011000=>9
100011001=>9
100011010=>9
100011011=>9
100011100=>9
100011101=>9
100011110=>9
100011111=>9
100100000=>9
100100001=>9
100100010=>9
100100011=>9
100100100=>3
100100101=>9
100100110=>9
100100111=>9
100101000=>9
100101001=>9
100101010=>9
100101011=>9
100101100=>9
100101101=>9
100101110=>9
100101111=>9
100110000=>9
100110001=>9
100110010=>9
100110011=>9
100110100=>9
100110101=>9
100110110=>9
100110111=>9
100111000=>9
100111001=>9
100111010=>9
100111011=>9
100111100=>9
100111101=>9
100111110=>9
100111111=>9
101000000=>9
101000001=>9
101000010=>9
101000011=>9
101000100=>9
101000101=>9
101000110=>9
101000111=>9
101001000=>9
101001001=>9
101001010=>9
101001011=>9
101001100=>9
101001101=>9
101001110=>9
101001111=>9
101010000=>9
101010001=>9
101010010=>9
101010011=>9
101010100=>9
101010101=>9
101010110=>9
101010111=>9
101011000=>9
101011001=>9
101011010=>9
101011011=>9
101011100=>9
101011101=>9
101011110=>9
101011111=>9
101100000=>9
101100001=>9
101100010=>9
101100011=>9
101100100=>9
101100101=>9
101100110=>9
101100111=>9
101101000=>9
101101001=>9
101101010=>9
101101011=>9
101101100=>9
101101101=>3
101101110=>9
101101111=>9
101110000=>9
101110001=>9
101110010=>9
101110011=>9
101110100=>9
101110101=>9
101110110=>9
101110111=>9
101111000=>9
101111001=>9
101111010=>9
101111011=>9
101111100=>9
101111101=>9
101111110=>9
101111111=>9
110000000=>9
110000001=>9
110000010=>9
110000011=>9
110000100=>9
110000101=>9
110000110=>9
110000111=>9
110001000=>9
110001001=>9
110001010=>9
110001011=>9
110001100=>9
110001101=>9
110001110=>9
110001111=>9
110010000=>9
110010001=>9
110010010=>9
110010011=>9
110010100=>9
110010101=>9
110010110=>9
110010111=>9
110011000=>9
110011001=>9
110011010=>9
110011011=>9
110011100=>9
110011101=>9
110011110=>9
110011111=>9
110100000=>9
110100001=>9
110100010=>9
110100011=>9
110100100=>9
110100101=>9
110100110=>9
110100111=>9
110101000=>9
110101001=>9
110101010=>9
110101011=>9
110101100=>9
110101101=>9
110101110=>9
110101111=>9
110110000=>9
110110001=>9
110110010=>9
110110011=>9
110110100=>9
110110101=>9
110110110=>3
110110111=>9
110111000=>9
110111001=>9
110111010=>9
110111011=>9
110111100=>9
110111101=>9
110111110=>9
110111111=>9
111000000=>9
111000001=>9
111000010=>9
111000011=>9
111000100=>9
111000101=>9
111000110=>9
111000111=>9
111001000=>9
111001001=>9
111001010=>9
111001011=>9
111001100=>9
111001101=>9
111001110=>9
111001111=>9
111010000=>9
111010001=>9
111010010=>9
111010011=>9
111010100=>9
111010101=>9
111010110=>9
111010111=>9
111011000=>9
111011001=>9
111011010=>9
111011011=>9
111011100=>9
111011101=>9
111011110=>9
111011111=>9
111100000=>9
111100001=>9
111100010=>9
111100011=>9
111100100=>9
111100101=>9
111100110=>9
111100111=>9
111101000=>9
111101001=>9
111101010=>9
111101011=>9
111101100=>9
111101101=>9
111101110=>9
111101111=>9
111110000=>9
111110001=>9
111110010=>9
111110011=>9
111110100=>9
111110101=>9
111110110=>9
111110111=>9
111111000=>9
111111001=>9
111111010=>9
111111011=>9
111111100=>9
111111101=>9
111111110=>9
111111111=>1
0000000001=>10
0010000001=>10
0010101101=>10
0010101011=>10
0010100111=>10
0010011101=>10
0010011011=>10
0010010111=>10
0010001111=>10
0001110101=>10
0001110011=>10
0001101101=>10
0001101011=>10
0001100111=>10
0001011101=>10
0001011011=>10
0001010111=>10
0001001111=>10
0000111101=>10
0000111011=>10
0000110111=>10
0000101111=>10
0000011111=>10
0000000000=>1
0000000110=>10
0000011000=>10
0000011110=>10
0000010010=>10
0001100000=>10
0001100110=>10
0001111000=>10
0001111110=>10
0001110010=>10
0001001000=>10
0001001110=>10
0001000010=>5
0001011010=>10
0010101010=>10
0010101000=>10
0010101100=>10
0010100100=>10
0010010100=>10
0001010100=>10
0010101110=>10
0010100000=>10
0010000100=>5
0000010100=>10
0000000010=>10
0000001110=>10
0000111110=>10
0000000100=>10
0000001010=>10
0000010110=>10
0000101110=>10
0001011110=>10
0001101110=>10
0001110110=>10
0001111010=>10
0001111100=>10
0000000101=>10
0000001101=>10
0000011101=>10
0001111101=>10
0000001001=>10
0000010101=>10
0000101101=>10
0010110001=>10
0001100001=>10
0001000001=>10
0000111111=>10
0001110100=>10
0001101100=>10
0010011100=>10
0001011100=>10
0000111100=>10
0001101010=>10
0010011010=>10
0000111010=>10
0010100110=>10
0010010110=>10
0001010110=>10
0000110110=>10
0010001110=>10
0001101001=>10
0000110001=>10
0000010001=>10
0000001100=>10
0000011001=>10
0000110011=>10
0000110100=>10
0000000011=>10
0000011011=>10
0001101111=>10
0000110101=>10
0010000010=>10
0001000011=>10
0010011110=>10
0001010000=>10
0001000100=>10
0001010101=>10
0001001011=>10
0001100011=>5
0001110111=>10
0010000000=>10
0000000111=>10
0000001111=>10
0001111111=>10
0000001011=>10
0000010111=>10
0001011111=>10
0001111001=>10
0000011010=>10
0000101010=>10
0000100101=>10
0010010001=>10
0010000101=>10
0010010101=>10
0010010011=>10
0000101011=>10
0001000111=>10
0000100111=>10
0010010010=>10
0001001010=>10
0001001001=>10
0001000101=>10
0000100011=>10
0000100100=>10
0000100010=>10
0010110000=>10
0000011100=>10
0000001000=>10
0000101100=>10
0010101111=>10
0000101000=>10
0010001000=>10
0001001100=>10
0001000110=>10
0001100100=>10
0001100010=>10
0000100110=>10
0000110010=>10
0010010000=>10
0001010010=>10
0001000000=>10
0001011001=>10
0001100101=>10
0001110001=>10
0010011001=>10
0010100101=>5
0010101001=>10
0010011111=>10
0000111001=>10
0010001101=>10
0001001101=>10
0001010001=>10
0001010011=>10
0001111011=>10
0010011000=>10
0001011000=>10
0000100000=>10
0010001011=>10
0010000111=>10
0000010011=>10
0010001100=>10
0010000110=>10
0000110000=>10
0000100001=>5
0010100011=>10
0010100001=>10
0000111000=>10
0001101000=>10
0000010000=>10
0000101001=>10
0010100010=>10
0010001001=>10
0010000011=>10
0010001010=>10
0001110000=>10
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
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
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!