Identifier
Identifier
Values
0 => 0
1 => 0
00 => 0
01 => 0
10 => 1
11 => 0
000 => 0
001 => 0
010 => 1
011 => 0
100 => 2
101 => 1
110 => 2
111 => 0
0000 => 0
0001 => 0
0010 => 1
0011 => 0
0100 => 2
0101 => 0
0110 => 1
0111 => 0
1000 => 3
1001 => 2
1010 => 1
1011 => 1
1100 => 3
1101 => 2
1110 => 3
1111 => 0
00000 => 0
00001 => 0
00010 => 1
00011 => 0
00100 => 2
00101 => 0
00110 => 1
00111 => 0
01000 => 3
01001 => 1
01010 => 2
01011 => 0
01100 => 2
01101 => 1
01110 => 1
01111 => 0
10000 => 4
10001 => 3
10010 => 3
10011 => 2
10100 => 4
10101 => 2
10110 => 3
10111 => 1
11000 => 4
11001 => 3
11010 => 4
11011 => 2
11100 => 4
11101 => 3
11110 => 4
11111 => 0
000000 => 0
000001 => 0
000010 => 1
000011 => 0
000100 => 2
000101 => 0
000110 => 1
000111 => 0
001000 => 3
001001 => 0
001010 => 1
001011 => 0
001100 => 2
001101 => 0
001110 => 1
001111 => 0
010000 => 4
010001 => 2
010010 => 1
010011 => 1
010100 => 3
010101 => 0
010110 => 1
010111 => 0
011000 => 3
011001 => 2
011010 => 2
011011 => 0
011100 => 2
011101 => 1
011110 => 1
011111 => 0
100000 => 5
100001 => 4
100010 => 4
100011 => 3
100100 => 2
100101 => 3
100110 => 3
100111 => 2
101000 => 5
101001 => 4
101010 => 1
101011 => 2
101100 => 4
101101 => 1
101110 => 3
101111 => 1
110000 => 5
110001 => 4
110010 => 5
110011 => 3
110100 => 5
110101 => 4
110110 => 2
110111 => 2
111000 => 5
111001 => 4
111010 => 5
111011 => 3
111100 => 5
111101 => 4
111110 => 5
111111 => 0
0000000 => 0
0000001 => 0
0000010 => 1
0000011 => 0
0000100 => 2
0000101 => 0
0000110 => 1
0000111 => 0
0001000 => 3
0001001 => 0
0001010 => 1
0001011 => 0
0001100 => 2
0001101 => 0
0001110 => 1
0001111 => 0
0010000 => 4
0010001 => 1
0010010 => 2
0010011 => 0
0010100 => 2
0010101 => 0
0010110 => 1
0010111 => 0
0011000 => 3
0011001 => 1
0011010 => 1
0011011 => 0
0011100 => 2
0011101 => 0
0011110 => 1
0011111 => 0
0100000 => 5
0100001 => 3
0100010 => 3
0100011 => 2
0100100 => 4
0100101 => 1
0100110 => 2
0100111 => 1
0101000 => 4
0101001 => 2
0101010 => 3
0101011 => 0
0101100 => 2
0101101 => 1
0101110 => 1
0101111 => 0
0110000 => 4
0110001 => 3
0110010 => 3
0110011 => 1
0110100 => 3
0110101 => 2
0110110 => 2
0110111 => 0
0111000 => 3
0111001 => 2
0111010 => 2
0111011 => 1
0111100 => 2
0111101 => 1
0111110 => 1
0111111 => 0
1000000 => 6
1000001 => 5
1000010 => 5
1000011 => 4
1000100 => 5
1000101 => 4
1000110 => 4
1000111 => 3
1001000 => 6
1001001 => 4
1001010 => 4
1001011 => 3
1001100 => 5
1001101 => 3
1001110 => 3
1001111 => 2
1010000 => 6
1010001 => 5
1010010 => 5
1010011 => 4
1010100 => 6
1010101 => 3
1010110 => 4
1010111 => 2
1011000 => 5
1011001 => 4
1011010 => 5
1011011 => 2
1011100 => 4
1011101 => 3
1011110 => 3
1011111 => 1
1100000 => 6
1100001 => 5
1100010 => 6
1100011 => 4
1100100 => 6
1100101 => 5
1100110 => 5
1100111 => 3
1101000 => 6
1101001 => 5
1101010 => 6
1101011 => 4
1101100 => 6
1101101 => 4
1101110 => 5
1101111 => 2
1110000 => 6
1110001 => 5
1110010 => 6
1110011 => 4
1110100 => 6
1110101 => 5
1110110 => 6
1110111 => 3
1111000 => 6
1111001 => 5
1111010 => 6
1111011 => 4
1111100 => 6
1111101 => 5
1111110 => 6
1111111 => 0
00000000 => 0
00000001 => 0
00000010 => 1
00000011 => 0
00000100 => 2
00000101 => 0
00000110 => 1
00000111 => 0
00001000 => 3
00001001 => 0
00001010 => 1
00001011 => 0
00001100 => 2
00001101 => 0
00001110 => 1
00001111 => 0
00010000 => 4
00010001 => 0
00010010 => 1
00010011 => 0
00010100 => 2
00010101 => 0
00010110 => 1
00010111 => 0
00011000 => 3
00011001 => 0
00011010 => 1
00011011 => 0
00011100 => 2
00011101 => 0
00011110 => 1
00011111 => 0
00100000 => 5
00100001 => 2
00100010 => 1
00100011 => 1
00100100 => 3
00100101 => 0
00100110 => 1
00100111 => 0
00101000 => 3
00101001 => 1
00101010 => 1
00101011 => 0
00101100 => 2
00101101 => 0
00101110 => 1
00101111 => 0
00110000 => 4
00110001 => 2
00110010 => 2
00110011 => 0
00110100 => 2
00110101 => 0
00110110 => 1
00110111 => 0
00111000 => 3
00111001 => 1
00111010 => 1
00111011 => 0
00111100 => 2
00111101 => 0
00111110 => 1
00111111 => 0
01000000 => 6
01000001 => 4
01000010 => 4
01000011 => 3
01000100 => 2
01000101 => 2
01000110 => 3
01000111 => 2
01001000 => 5
01001001 => 2
01001010 => 3
01001011 => 1
01001100 => 3
01001101 => 1
01001110 => 2
01001111 => 1
01010000 => 5
01010001 => 3
01010010 => 4
01010011 => 2
01010100 => 4
01010101 => 0
01010110 => 1
01010111 => 0
01011000 => 3
01011001 => 2
01011010 => 2
01011011 => 0
01011100 => 2
01011101 => 1
01011110 => 1
01011111 => 0
01100000 => 5
01100001 => 4
01100010 => 4
01100011 => 2
01100100 => 4
01100101 => 3
01100110 => 1
01100111 => 1
01101000 => 4
01101001 => 3
01101010 => 3
01101011 => 1
01101100 => 3
01101101 => 2
01101110 => 1
01101111 => 0
01110000 => 4
01110001 => 3
01110010 => 3
01110011 => 2
01110100 => 3
01110101 => 2
01110110 => 2
01110111 => 0
01111000 => 3
01111001 => 2
01111010 => 2
01111011 => 1
01111100 => 2
01111101 => 1
01111110 => 1
01111111 => 0
10000000 => 7
10000001 => 6
10000010 => 6
10000011 => 5
10000100 => 6
10000101 => 5
10000110 => 5
10000111 => 4
10001000 => 3
10001001 => 5
10001010 => 5
10001011 => 4
10001100 => 5
10001101 => 4
10001110 => 4
10001111 => 3
10010000 => 7
10010001 => 6
10010010 => 5
10010011 => 4
10010100 => 6
10010101 => 4
10010110 => 4
10010111 => 3
10011000 => 6
10011001 => 2
10011010 => 4
10011011 => 3
10011100 => 5
10011101 => 3
10011110 => 3
10011111 => 2
10100000 => 7
10100001 => 6
10100010 => 6
10100011 => 5
10100100 => 7
10100101 => 5
10100110 => 5
10100111 => 4
10101000 => 7
10101001 => 6
10101010 => 1
10101011 => 3
10101100 => 5
10101101 => 3
10101110 => 4
10101111 => 2
10110000 => 6
10110001 => 5
10110010 => 6
10110011 => 4
10110100 => 6
10110101 => 4
10110110 => 5
10110111 => 2
10111000 => 5
10111001 => 4
10111010 => 5
10111011 => 1
10111100 => 4
10111101 => 3
10111110 => 3
10111111 => 1
11000000 => 7
11000001 => 6
11000010 => 7
11000011 => 5
11000100 => 7
11000101 => 6
11000110 => 6
11000111 => 4
11001000 => 7
11001001 => 6
11001010 => 7
11001011 => 5
11001100 => 3
11001101 => 5
11001110 => 5
11001111 => 3
11010000 => 7
11010001 => 6
11010010 => 7
11010011 => 5
11010100 => 7
11010101 => 6
11010110 => 6
11010111 => 4
11011000 => 7
11011001 => 6
11011010 => 7
11011011 => 4
11011100 => 6
11011101 => 2
11011110 => 5
11011111 => 2
11100000 => 7
11100001 => 6
11100010 => 7
11100011 => 5
11100100 => 7
11100101 => 6
11100110 => 7
11100111 => 4
11101000 => 7
11101001 => 6
11101010 => 7
11101011 => 5
11101100 => 7
11101101 => 6
11101110 => 3
11101111 => 3
11110000 => 7
11110001 => 6
11110010 => 7
11110011 => 5
11110100 => 7
11110101 => 6
11110110 => 7
11110111 => 4
11111000 => 7
11111001 => 6
11111010 => 7
11111011 => 5
11111100 => 7
11111101 => 6
11111110 => 7
11111111 => 0
000000000 => 0
000000001 => 0
000000010 => 1
000000011 => 0
000000100 => 2
000000101 => 0
000000110 => 1
000000111 => 0
000001000 => 3
000001001 => 0
000001010 => 1
000001011 => 0
000001100 => 2
000001101 => 0
000001110 => 1
000001111 => 0
000010000 => 4
000010001 => 0
000010010 => 1
000010011 => 0
000010100 => 2
000010101 => 0
000010110 => 1
000010111 => 0
000011000 => 3
000011001 => 0
000011010 => 1
000011011 => 0
000011100 => 2
000011101 => 0
000011110 => 1
000011111 => 0
000100000 => 5
000100001 => 1
000100010 => 2
000100011 => 0
000100100 => 2
000100101 => 0
000100110 => 1
000100111 => 0
000101000 => 3
000101001 => 0
000101010 => 1
000101011 => 0
000101100 => 2
000101101 => 0
000101110 => 1
000101111 => 0
000110000 => 4
000110001 => 1
000110010 => 1
000110011 => 0
000110100 => 2
000110101 => 0
000110110 => 1
000110111 => 0
000111000 => 3
000111001 => 0
000111010 => 1
000111011 => 0
000111100 => 2
000111101 => 0
000111110 => 1
000111111 => 0
001000000 => 6
001000001 => 3
001000010 => 3
001000011 => 2
001000100 => 4
001000101 => 1
001000110 => 2
001000111 => 1
001001000 => 4
001001001 => 0
001001010 => 1
001001011 => 0
001001100 => 2
001001101 => 0
001001110 => 1
001001111 => 0
001010000 => 4
001010001 => 2
001010010 => 2
001010011 => 0
001010100 => 2
001010101 => 0
001010110 => 1
001010111 => 0
001011000 => 3
001011001 => 1
001011010 => 1
001011011 => 0
001011100 => 2
001011101 => 0
001011110 => 1
001011111 => 0
001100000 => 5
001100001 => 3
001100010 => 3
001100011 => 1
001100100 => 3
001100101 => 1
001100110 => 2
001100111 => 0
001101000 => 3
001101001 => 1
001101010 => 1
001101011 => 0
001101100 => 2
001101101 => 0
001101110 => 1
001101111 => 0
001110000 => 4
001110001 => 2
001110010 => 2
001110011 => 1
001110100 => 2
001110101 => 0
001110110 => 1
001110111 => 0
001111000 => 3
001111001 => 1
001111010 => 1
001111011 => 0
001111100 => 2
001111101 => 0
001111110 => 1
001111111 => 0
010000000 => 7
010000001 => 5
010000010 => 5
010000011 => 4
010000100 => 5
010000101 => 3
010000110 => 4
010000111 => 3
010001000 => 6
010001001 => 3
010001010 => 3
010001011 => 2
010001100 => 4
010001101 => 2
010001110 => 3
010001111 => 2
010010000 => 6
010010001 => 4
010010010 => 1
010010011 => 2
010010100 => 4
010010101 => 1
010010110 => 2
010010111 => 1
010011000 => 4
010011001 => 2
010011010 => 3
010011011 => 1
010011100 => 3
010011101 => 1
010011110 => 2
010011111 => 1
010100000 => 6
010100001 => 4
010100010 => 5
010100011 => 3
010100100 => 5
010100101 => 2
010100110 => 3
010100111 => 2
010101000 => 5
010101001 => 3
010101010 => 4
010101011 => 0
010101100 => 2
010101101 => 1
010101110 => 1
010101111 => 0
010110000 => 4
010110001 => 3
010110010 => 3
010110011 => 1
010110100 => 3
010110101 => 2
010110110 => 1
010110111 => 0
010111000 => 3
010111001 => 2
010111010 => 2
010111011 => 0
010111100 => 2
010111101 => 1
010111110 => 1
010111111 => 0
011000000 => 6
011000001 => 5
011000010 => 5
011000011 => 3
011000100 => 5
011000101 => 4
011000110 => 3
011000111 => 2
011001000 => 5
011001001 => 4
011001010 => 4
011001011 => 2
011001100 => 4
011001101 => 2
011001110 => 2
011001111 => 1
011010000 => 5
011010001 => 4
011010010 => 4
011010011 => 2
011010100 => 4
011010101 => 3
011010110 => 3
011010111 => 1
011011000 => 4
011011001 => 3
011011010 => 3
011011011 => 0
011011100 => 2
011011101 => 1
011011110 => 1
011011111 => 0
011100000 => 5
011100001 => 4
011100010 => 4
011100011 => 3
011100100 => 4
011100101 => 3
011100110 => 3
011100111 => 1
011101000 => 4
011101001 => 3
011101010 => 3
011101011 => 2
011101100 => 3
011101101 => 2
011101110 => 2
011101111 => 0
011110000 => 4
011110001 => 3
011110010 => 3
011110011 => 2
011110100 => 3
011110101 => 2
011110110 => 2
011110111 => 1
011111000 => 3
011111001 => 2
011111010 => 2
011111011 => 1
011111100 => 2
011111101 => 1
011111110 => 1
011111111 => 0
100000000 => 8
100000001 => 7
100000010 => 7
100000011 => 6
100000100 => 7
100000101 => 6
100000110 => 6
100000111 => 5
100001000 => 7
100001001 => 6
100001010 => 6
100001011 => 5
100001100 => 6
100001101 => 5
100001110 => 5
100001111 => 4
100010000 => 8
100010001 => 6
100010010 => 6
100010011 => 5
100010100 => 6
100010101 => 5
100010110 => 5
100010111 => 4
100011000 => 7
100011001 => 5
100011010 => 5
100011011 => 4
100011100 => 5
100011101 => 4
100011110 => 4
100011111 => 3
100100000 => 8
100100001 => 7
100100010 => 7
100100011 => 6
100100100 => 2
100100101 => 5
100100110 => 5
100100111 => 4
100101000 => 7
100101001 => 5
100101010 => 5
100101011 => 4
100101100 => 6
100101101 => 4
100101110 => 4
100101111 => 3
100110000 => 7
100110001 => 6
100110010 => 6
100110011 => 4
100110100 => 6
100110101 => 4
100110110 => 4
100110111 => 3
100111000 => 6
100111001 => 5
100111010 => 4
100111011 => 3
100111100 => 5
100111101 => 3
100111110 => 3
100111111 => 2
101000000 => 8
101000001 => 7
101000010 => 7
101000011 => 6
101000100 => 8
101000101 => 6
101000110 => 6
101000111 => 5
101001000 => 8
101001001 => 7
101001010 => 6
101001011 => 5
101001100 => 7
101001101 => 5
101001110 => 5
101001111 => 4
101010000 => 8
101010001 => 7
101010010 => 7
101010011 => 6
101010100 => 8
101010101 => 4
101010110 => 5
101010111 => 3
101011000 => 6
101011001 => 5
101011010 => 6
101011011 => 3
101011100 => 5
101011101 => 3
101011110 => 4
101011111 => 2
101100000 => 7
101100001 => 6
101100010 => 7
101100011 => 5
101100100 => 7
101100101 => 5
101100110 => 6
101100111 => 4
101101000 => 7
101101001 => 6
101101010 => 7
101101011 => 4
101101100 => 6
101101101 => 1
101101110 => 4
101101111 => 2
101110000 => 6
101110001 => 5
101110010 => 6
101110011 => 4
101110100 => 6
101110101 => 5
101110110 => 5
101110111 => 2
101111000 => 5
101111001 => 4
101111010 => 5
101111011 => 3
101111100 => 4
101111101 => 3
101111110 => 3
101111111 => 1
110000000 => 8
110000001 => 7
110000010 => 8
110000011 => 6
110000100 => 8
110000101 => 7
110000110 => 7
110000111 => 5
110001000 => 8
110001001 => 7
110001010 => 8
110001011 => 6
110001100 => 7
110001101 => 6
110001110 => 6
110001111 => 4
110010000 => 8
110010001 => 7
110010010 => 8
110010011 => 6
110010100 => 8
110010101 => 7
110010110 => 7
110010111 => 5
110011000 => 8
110011001 => 6
110011010 => 7
110011011 => 5
110011100 => 7
110011101 => 5
110011110 => 5
110011111 => 3
110100000 => 8
110100001 => 7
110100010 => 8
110100011 => 6
110100100 => 8
110100101 => 7
110100110 => 7
110100111 => 5
110101000 => 8
110101001 => 7
110101010 => 8
110101011 => 6
110101100 => 8
110101101 => 6
110101110 => 6
110101111 => 4
110110000 => 8
110110001 => 7
110110010 => 8
110110011 => 6
110110100 => 8
110110101 => 7
110110110 => 2
110110111 => 4
110111000 => 7
110111001 => 6
110111010 => 7
110111011 => 4
110111100 => 6
110111101 => 5
110111110 => 5
110111111 => 2
111000000 => 8
111000001 => 7
111000010 => 8
111000011 => 6
111000100 => 8
111000101 => 7
111000110 => 8
111000111 => 5
111001000 => 8
111001001 => 7
111001010 => 8
111001011 => 6
111001100 => 8
111001101 => 7
111001110 => 7
111001111 => 4
111010000 => 8
111010001 => 7
111010010 => 8
111010011 => 6
111010100 => 8
111010101 => 7
111010110 => 8
111010111 => 5
111011000 => 8
111011001 => 7
111011010 => 8
111011011 => 6
111011100 => 8
111011101 => 6
111011110 => 7
111011111 => 3
111100000 => 8
111100001 => 7
111100010 => 8
111100011 => 6
111100100 => 8
111100101 => 7
111100110 => 8
111100111 => 5
111101000 => 8
111101001 => 7
111101010 => 8
111101011 => 6
111101100 => 8
111101101 => 7
111101110 => 8
111101111 => 4
111110000 => 8
111110001 => 7
111110010 => 8
111110011 => 6
111110100 => 8
111110101 => 7
111110110 => 8
111110111 => 5
111111000 => 8
111111001 => 7
111111010 => 8
111111011 => 6
111111100 => 8
111111101 => 7
111111110 => 8
111111111 => 0
click to show generating function       
Description
The index of a given binary word in the lex-order among all its cyclic shifts.
References
[1] Ahlbach, C., Swanson, J. P. Refined cyclic sieving on words for the major index statistic MathSciNet:3836732
Code
def statistic(w):
    orbit = [ tuple(w[i:] + w[:i]) for i in range(len(w)) ]
    return sorted(set(orbit)).index(tuple(w))

Created
Jul 02, 2019 at 10:59 by Christian Stump
Updated
Jul 02, 2019 at 10:59 by Christian Stump