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Identifier
Values
=>
0=>0 1=>0 00=>0 01=>0 10=>1 11=>0 000=>0 001=>0 010=>2 011=>0 100=>1 101=>1 110=>2 111=>0 0000=>0 0001=>0 0010=>3 0011=>0 0100=>2 0101=>2 0110=>3 0111=>0 1000=>1 1001=>1 1010=>0 1011=>1 1100=>2 1101=>2 1110=>3 1111=>0 00000=>0 00001=>0 00010=>4 00011=>0 00100=>3 00101=>3 00110=>4 00111=>0 01000=>2 01001=>2 01010=>1 01011=>2 01100=>3 01101=>3 01110=>4 01111=>0 10000=>1 10001=>1 10010=>0 10011=>1 10100=>4 10101=>4 10110=>0 10111=>1 11000=>2 11001=>2 11010=>1 11011=>2 11100=>3 11101=>3 11110=>4 11111=>0 000000=>0 000001=>0 000010=>5 000011=>0 000100=>4 000101=>4 000110=>5 000111=>0 001000=>3 001001=>3 001010=>2 001011=>3 001100=>4 001101=>4 001110=>5 001111=>0 010000=>2 010001=>2 010010=>1 010011=>2 010100=>0 010101=>0 010110=>1 010111=>2 011000=>3 011001=>3 011010=>2 011011=>3 011100=>4 011101=>4 011110=>5 011111=>0 100000=>1 100001=>1 100010=>0 100011=>1 100100=>5 100101=>5 100110=>0 100111=>1 101000=>4 101001=>4 101010=>3 101011=>4 101100=>5 101101=>5 101110=>0 101111=>1 110000=>2 110001=>2 110010=>1 110011=>2 110100=>0 110101=>0 110110=>1 110111=>2 111000=>3 111001=>3 111010=>2 111011=>3 111100=>4 111101=>4 111110=>5 111111=>0 0000000=>0 0000001=>0 0000010=>6 0000011=>0 0000100=>5 0000101=>5 0000110=>6 0000111=>0 0001000=>4 0001001=>4 0001010=>3 0001011=>4 0001100=>5 0001101=>5 0001110=>6 0001111=>0 0010000=>3 0010001=>3 0010010=>2 0010011=>3 0010100=>1 0010101=>1 0010110=>2 0010111=>3 0011000=>4 0011001=>4 0011010=>3 0011011=>4 0011100=>5 0011101=>5 0011110=>6 0011111=>0 0100000=>2 0100001=>2 0100010=>1 0100011=>2 0100100=>0 0100101=>0 0100110=>1 0100111=>2 0101000=>6 0101001=>6 0101010=>5 0101011=>6 0101100=>0 0101101=>0 0101110=>1 0101111=>2 0110000=>3 0110001=>3 0110010=>2 0110011=>3 0110100=>1 0110101=>1 0110110=>2 0110111=>3 0111000=>4 0111001=>4 0111010=>3 0111011=>4 0111100=>5 0111101=>5 0111110=>6 0111111=>0 1000000=>1 1000001=>1 1000010=>0 1000011=>1 1000100=>6 1000101=>6 1000110=>0 1000111=>1 1001000=>5 1001001=>5 1001010=>4 1001011=>5 1001100=>6 1001101=>6 1001110=>0 1001111=>1 1010000=>4 1010001=>4 1010010=>3 1010011=>4 1010100=>2 1010101=>2 1010110=>3 1010111=>4 1011000=>5 1011001=>5 1011010=>4 1011011=>5 1011100=>6 1011101=>6 1011110=>0 1011111=>1 1100000=>2 1100001=>2 1100010=>1 1100011=>2 1100100=>0 1100101=>0 1100110=>1 1100111=>2 1101000=>6 1101001=>6 1101010=>5 1101011=>6 1101100=>0 1101101=>0 1101110=>1 1101111=>2 1110000=>3 1110001=>3 1110010=>2 1110011=>3 1110100=>1 1110101=>1 1110110=>2 1110111=>3 1111000=>4 1111001=>4 1111010=>3 1111011=>4 1111100=>5 1111101=>5 1111110=>6 1111111=>0 00000000=>0 00000001=>0 00000010=>7 00000011=>0 00000100=>6 00000101=>6 00000110=>7 00000111=>0 00001000=>5 00001001=>5 00001010=>4 00001011=>5 00001100=>6 00001101=>6 00001110=>7 00001111=>0 00010000=>4 00010001=>4 00010010=>3 00010011=>4 00010100=>2 00010101=>2 00010110=>3 00010111=>4 00011000=>5 00011001=>5 00011010=>4 00011011=>5 00011100=>6 00011101=>6 00011110=>7 00011111=>0 00100000=>3 00100001=>3 00100010=>2 00100011=>3 00100100=>1 00100101=>1 00100110=>2 00100111=>3 00101000=>0 00101001=>0 00101010=>7 00101011=>0 00101100=>1 00101101=>1 00101110=>2 00101111=>3 00110000=>4 00110001=>4 00110010=>3 00110011=>4 00110100=>2 00110101=>2 00110110=>3 00110111=>4 00111000=>5 00111001=>5 00111010=>4 00111011=>5 00111100=>6 00111101=>6 00111110=>7 00111111=>0 01000000=>2 01000001=>2 01000010=>1 01000011=>2 01000100=>0 01000101=>0 01000110=>1 01000111=>2 01001000=>7 01001001=>7 01001010=>6 01001011=>7 01001100=>0 01001101=>0 01001110=>1 01001111=>2 01010000=>6 01010001=>6 01010010=>5 01010011=>6 01010100=>4 01010101=>4 01010110=>5 01010111=>6 01011000=>7 01011001=>7 01011010=>6 01011011=>7 01011100=>0 01011101=>0 01011110=>1 01011111=>2 01100000=>3 01100001=>3 01100010=>2 01100011=>3 01100100=>1 01100101=>1 01100110=>2 01100111=>3 01101000=>0 01101001=>0 01101010=>7 01101011=>0 01101100=>1 01101101=>1 01101110=>2 01101111=>3 01110000=>4 01110001=>4 01110010=>3 01110011=>4 01110100=>2 01110101=>2 01110110=>3 01110111=>4 01111000=>5 01111001=>5 01111010=>4 01111011=>5 01111100=>6 01111101=>6 01111110=>7 01111111=>0 10000000=>1 10000001=>1 10000010=>0 10000011=>1 10000100=>7 10000101=>7 10000110=>0 10000111=>1 10001000=>6 10001001=>6 10001010=>5 10001011=>6 10001100=>7 10001101=>7 10001110=>0 10001111=>1 10010000=>5 10010001=>5 10010010=>4 10010011=>5 10010100=>3 10010101=>3 10010110=>4 10010111=>5 10011000=>6 10011001=>6 10011010=>5 10011011=>6 10011100=>7 10011101=>7 10011110=>0 10011111=>1 10100000=>4 10100001=>4 10100010=>3 10100011=>4 10100100=>2 10100101=>2 10100110=>3 10100111=>4 10101000=>1 10101001=>1 10101010=>0 10101011=>1 10101100=>2 10101101=>2 10101110=>3 10101111=>4 10110000=>5 10110001=>5 10110010=>4 10110011=>5 10110100=>3 10110101=>3 10110110=>4 10110111=>5 10111000=>6 10111001=>6 10111010=>5 10111011=>6 10111100=>7 10111101=>7 10111110=>0 10111111=>1 11000000=>2 11000001=>2 11000010=>1 11000011=>2 11000100=>0 11000101=>0 11000110=>1 11000111=>2 11001000=>7 11001001=>7 11001010=>6 11001011=>7 11001100=>0 11001101=>0 11001110=>1 11001111=>2 11010000=>6 11010001=>6 11010010=>5 11010011=>6 11010100=>4 11010101=>4 11010110=>5 11010111=>6 11011000=>7 11011001=>7 11011010=>6 11011011=>7 11011100=>0 11011101=>0 11011110=>1 11011111=>2 11100000=>3 11100001=>3 11100010=>2 11100011=>3 11100100=>1 11100101=>1 11100110=>2 11100111=>3 11101000=>0 11101001=>0 11101010=>7 11101011=>0 11101100=>1 11101101=>1 11101110=>2 11101111=>3 11110000=>4 11110001=>4 11110010=>3 11110011=>4 11110100=>2 11110101=>2 11110110=>3 11110111=>4 11111000=>5 11111001=>5 11111010=>4 11111011=>5 11111100=>6 11111101=>6 11111110=>7 11111111=>0 000000000=>0 000000001=>0 000000010=>8 000000011=>0 000000100=>7 000000101=>7 000000110=>8 000000111=>0 000001000=>6 000001001=>6 000001010=>5 000001011=>6 000001100=>7 000001101=>7 000001110=>8 000001111=>0 000010000=>5 000010001=>5 000010010=>4 000010011=>5 000010100=>3 000010101=>3 000010110=>4 000010111=>5 000011000=>6 000011001=>6 000011010=>5 000011011=>6 000011100=>7 000011101=>7 000011110=>8 000011111=>0 000100000=>4 000100001=>4 000100010=>3 000100011=>4 000100100=>2 000100101=>2 000100110=>3 000100111=>4 000101000=>1 000101001=>1 000101010=>0 000101011=>1 000101100=>2 000101101=>2 000101110=>3 000101111=>4 000110000=>5 000110001=>5 000110010=>4 000110011=>5 000110100=>3 000110101=>3 000110110=>4 000110111=>5 000111000=>6 000111001=>6 000111010=>5 000111011=>6 000111100=>7 000111101=>7 000111110=>8 000111111=>0 001000000=>3 001000001=>3 001000010=>2 001000011=>3 001000100=>1 001000101=>1 001000110=>2 001000111=>3 001001000=>0 001001001=>0 001001010=>8 001001011=>0 001001100=>1 001001101=>1 001001110=>2 001001111=>3 001010000=>8 001010001=>8 001010010=>7 001010011=>8 001010100=>6 001010101=>6 001010110=>7 001010111=>8 001011000=>0 001011001=>0 001011010=>8 001011011=>0 001011100=>1 001011101=>1 001011110=>2 001011111=>3 001100000=>4 001100001=>4 001100010=>3 001100011=>4 001100100=>2 001100101=>2 001100110=>3 001100111=>4 001101000=>1 001101001=>1 001101010=>0 001101011=>1 001101100=>2 001101101=>2 001101110=>3 001101111=>4 001110000=>5 001110001=>5 001110010=>4 001110011=>5 001110100=>3 001110101=>3 001110110=>4 001110111=>5 001111000=>6 001111001=>6 001111010=>5 001111011=>6 001111100=>7 001111101=>7 001111110=>8 001111111=>0 010000000=>2 010000001=>2 010000010=>1 010000011=>2 010000100=>0 010000101=>0 010000110=>1 010000111=>2 010001000=>8 010001001=>8 010001010=>7 010001011=>8 010001100=>0 010001101=>0 010001110=>1 010001111=>2 010010000=>7 010010001=>7 010010010=>6 010010011=>7 010010100=>5 010010101=>5 010010110=>6 010010111=>7 010011000=>8 010011001=>8 010011010=>7 010011011=>8 010011100=>0 010011101=>0 010011110=>1 010011111=>2 010100000=>6 010100001=>6 010100010=>5 010100011=>6 010100100=>4 010100101=>4 010100110=>5 010100111=>6 010101000=>3 010101001=>3 010101010=>2 010101011=>3 010101100=>4 010101101=>4 010101110=>5 010101111=>6 010110000=>7 010110001=>7 010110010=>6 010110011=>7 010110100=>5 010110101=>5 010110110=>6 010110111=>7 010111000=>8 010111001=>8 010111010=>7 010111011=>8 010111100=>0 010111101=>0 010111110=>1 010111111=>2 011000000=>3 011000001=>3 011000010=>2 011000011=>3 011000100=>1 011000101=>1 011000110=>2 011000111=>3 011001000=>0 011001001=>0 011001010=>8 011001011=>0 011001100=>1 011001101=>1 011001110=>2 011001111=>3 011010000=>8 011010001=>8 011010010=>7 011010011=>8 011010100=>6 011010101=>6 011010110=>7 011010111=>8 011011000=>0 011011001=>0 011011010=>8 011011011=>0 011011100=>1 011011101=>1 011011110=>2 011011111=>3 011100000=>4 011100001=>4 011100010=>3 011100011=>4 011100100=>2 011100101=>2 011100110=>3 011100111=>4 011101000=>1 011101001=>1 011101010=>0 011101011=>1 011101100=>2 011101101=>2 011101110=>3 011101111=>4 011110000=>5 011110001=>5 011110010=>4 011110011=>5 011110100=>3 011110101=>3 011110110=>4 011110111=>5 011111000=>6 011111001=>6 011111010=>5 011111011=>6 011111100=>7 011111101=>7 011111110=>8 011111111=>0 100000000=>1 100000001=>1 100000010=>0 100000011=>1 100000100=>8 100000101=>8 100000110=>0 100000111=>1 100001000=>7 100001001=>7 100001010=>6 100001011=>7 100001100=>8 100001101=>8 100001110=>0 100001111=>1 100010000=>6 100010001=>6 100010010=>5 100010011=>6 100010100=>4 100010101=>4 100010110=>5 100010111=>6 100011000=>7 100011001=>7 100011010=>6 100011011=>7 100011100=>8 100011101=>8 100011110=>0 100011111=>1 100100000=>5 100100001=>5 100100010=>4 100100011=>5 100100100=>3 100100101=>3 100100110=>4 100100111=>5 100101000=>2 100101001=>2 100101010=>1 100101011=>2 100101100=>3 100101101=>3 100101110=>4 100101111=>5 100110000=>6 100110001=>6 100110010=>5 100110011=>6 100110100=>4 100110101=>4 100110110=>5 100110111=>6 100111000=>7 100111001=>7 100111010=>6 100111011=>7 100111100=>8 100111101=>8 100111110=>0 100111111=>1 101000000=>4 101000001=>4 101000010=>3 101000011=>4 101000100=>2 101000101=>2 101000110=>3 101000111=>4 101001000=>1 101001001=>1 101001010=>0 101001011=>1 101001100=>2 101001101=>2 101001110=>3 101001111=>4 101010000=>0 101010001=>0 101010010=>8 101010011=>0 101010100=>7 101010101=>7 101010110=>8 101010111=>0 101011000=>1 101011001=>1 101011010=>0 101011011=>1 101011100=>2 101011101=>2 101011110=>3 101011111=>4 101100000=>5 101100001=>5 101100010=>4 101100011=>5 101100100=>3 101100101=>3 101100110=>4 101100111=>5 101101000=>2 101101001=>2 101101010=>1 101101011=>2 101101100=>3 101101101=>3 101101110=>4 101101111=>5 101110000=>6 101110001=>6 101110010=>5 101110011=>6 101110100=>4 101110101=>4 101110110=>5 101110111=>6 101111000=>7 101111001=>7 101111010=>6 101111011=>7 101111100=>8 101111101=>8 101111110=>0 101111111=>1 110000000=>2 110000001=>2 110000010=>1 110000011=>2 110000100=>0 110000101=>0 110000110=>1 110000111=>2 110001000=>8 110001001=>8 110001010=>7 110001011=>8 110001100=>0 110001101=>0 110001110=>1 110001111=>2 110010000=>7 110010001=>7 110010010=>6 110010011=>7 110010100=>5 110010101=>5 110010110=>6 110010111=>7 110011000=>8 110011001=>8 110011010=>7 110011011=>8 110011100=>0 110011101=>0 110011110=>1 110011111=>2 110100000=>6 110100001=>6 110100010=>5 110100011=>6 110100100=>4 110100101=>4 110100110=>5 110100111=>6 110101000=>3 110101001=>3 110101010=>2 110101011=>3 110101100=>4 110101101=>4 110101110=>5 110101111=>6 110110000=>7 110110001=>7 110110010=>6 110110011=>7 110110100=>5 110110101=>5 110110110=>6 110110111=>7 110111000=>8 110111001=>8 110111010=>7 110111011=>8 110111100=>0 110111101=>0 110111110=>1 110111111=>2 111000000=>3 111000001=>3 111000010=>2 111000011=>3 111000100=>1 111000101=>1 111000110=>2 111000111=>3 111001000=>0 111001001=>0 111001010=>8 111001011=>0 111001100=>1 111001101=>1 111001110=>2 111001111=>3 111010000=>8 111010001=>8 111010010=>7 111010011=>8 111010100=>6 111010101=>6 111010110=>7 111010111=>8 111011000=>0 111011001=>0 111011010=>8 111011011=>0 111011100=>1 111011101=>1 111011110=>2 111011111=>3 111100000=>4 111100001=>4 111100010=>3 111100011=>4 111100100=>2 111100101=>2 111100110=>3 111100111=>4 111101000=>1 111101001=>1 111101010=>0 111101011=>1 111101100=>2 111101101=>2 111101110=>3 111101111=>4 111110000=>5 111110001=>5 111110010=>4 111110011=>5 111110100=>3 111110101=>3 111110110=>4 111110111=>5 111111000=>6 111111001=>6 111111010=>5 111111011=>6 111111100=>7 111111101=>7 111111110=>8 111111111=>0
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Description
The modular major index of a binary word.
This is St000290The major index of a binary word. modulo the length of the word.
References
[1] Swanson, J. P. Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics MathSciNet:3885578
Code
def statistic(w):
    return w.major_index() % len(w)

Created
Oct 24, 2019 at 13:25 by Martin Rubey
Updated
Oct 24, 2019 at 13:25 by Martin Rubey