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Identifier
Values
=>
0=>1 1=>1 00=>2 01=>1 10=>2 11=>2 000=>3 001=>1 010=>2 011=>1 100=>3 101=>2 110=>3 111=>3 0000=>4 0001=>1 0010=>2 0011=>1 0100=>3 0101=>2 0110=>2 0111=>1 1000=>4 1001=>2 1010=>3 1011=>2 1100=>4 1101=>3 1110=>4 1111=>4 00000=>5 00001=>1 00010=>2 00011=>1 00100=>3 00101=>1 00110=>2 00111=>1 01000=>4 01001=>2 01010=>3 01011=>1 01100=>3 01101=>2 01110=>2 01111=>1 10000=>5 10001=>2 10010=>3 10011=>2 10100=>4 10101=>3 10110=>3 10111=>2 11000=>5 11001=>3 11010=>4 11011=>3 11100=>5 11101=>4 11110=>5 11111=>5 000000=>6 000001=>1 000010=>2 000011=>1 000100=>3 000101=>1 000110=>2 000111=>1 001000=>4 001001=>2 001010=>2 001011=>1 001100=>3 001101=>1 001110=>2 001111=>1 010000=>5 010001=>2 010010=>3 010011=>2 010100=>4 010101=>3 010110=>2 010111=>1 011000=>4 011001=>2 011010=>3 011011=>2 011100=>3 011101=>2 011110=>2 011111=>1 100000=>6 100001=>2 100010=>3 100011=>2 100100=>4 100101=>2 100110=>3 100111=>2 101000=>5 101001=>3 101010=>4 101011=>2 101100=>4 101101=>3 101110=>3 101111=>2 110000=>6 110001=>3 110010=>4 110011=>3 110100=>5 110101=>4 110110=>4 110111=>3 111000=>6 111001=>4 111010=>5 111011=>4 111100=>6 111101=>5 111110=>6 111111=>6 0000000=>7 0000001=>1 0000010=>2 0000011=>1 0000100=>3 0000101=>1 0000110=>2 0000111=>1 0001000=>4 0001001=>1 0001010=>2 0001011=>1 0001100=>3 0001101=>1 0001110=>2 0001111=>1 0010000=>5 0010001=>2 0010010=>3 0010011=>1 0010100=>3 0010101=>1 0010110=>2 0010111=>1 0011000=>4 0011001=>2 0011010=>2 0011011=>1 0011100=>3 0011101=>1 0011110=>2 0011111=>1 0100000=>6 0100001=>2 0100010=>3 0100011=>2 0100100=>4 0100101=>2 0100110=>3 0100111=>2 0101000=>5 0101001=>3 0101010=>4 0101011=>1 0101100=>3 0101101=>2 0101110=>2 0101111=>1 0110000=>5 0110001=>2 0110010=>3 0110011=>2 0110100=>4 0110101=>3 0110110=>3 0110111=>1 0111000=>4 0111001=>2 0111010=>3 0111011=>2 0111100=>3 0111101=>2 0111110=>2 0111111=>1 1000000=>7 1000001=>2 1000010=>3 1000011=>2 1000100=>4 1000101=>2 1000110=>3 1000111=>2 1001000=>5 1001001=>3 1001010=>3 1001011=>2 1001100=>4 1001101=>2 1001110=>3 1001111=>2 1010000=>6 1010001=>3 1010010=>4 1010011=>3 1010100=>5 1010101=>4 1010110=>3 1010111=>2 1011000=>5 1011001=>3 1011010=>4 1011011=>3 1011100=>4 1011101=>3 1011110=>3 1011111=>2 1100000=>7 1100001=>3 1100010=>4 1100011=>3 1100100=>5 1100101=>3 1100110=>4 1100111=>3 1101000=>6 1101001=>4 1101010=>5 1101011=>3 1101100=>5 1101101=>4 1101110=>4 1101111=>3 1110000=>7 1110001=>4 1110010=>5 1110011=>4 1110100=>6 1110101=>5 1110110=>5 1110111=>4 1111000=>7 1111001=>5 1111010=>6 1111011=>5 1111100=>7 1111101=>6 1111110=>7 1111111=>7 00000000=>8 00000001=>1 00000010=>2 00000011=>1 00000100=>3 00000101=>1 00000110=>2 00000111=>1 00001000=>4 00001001=>1 00001010=>2 00001011=>1 00001100=>3 00001101=>1 00001110=>2 00001111=>1 00010000=>5 00010001=>2 00010010=>2 00010011=>1 00010100=>3 00010101=>1 00010110=>2 00010111=>1 00011000=>4 00011001=>1 00011010=>2 00011011=>1 00011100=>3 00011101=>1 00011110=>2 00011111=>1 00100000=>6 00100001=>2 00100010=>3 00100011=>2 00100100=>4 00100101=>1 00100110=>2 00100111=>1 00101000=>4 00101001=>2 00101010=>2 00101011=>1 00101100=>3 00101101=>1 00101110=>2 00101111=>1 00110000=>5 00110001=>2 00110010=>3 00110011=>2 00110100=>3 00110101=>1 00110110=>2 00110111=>1 00111000=>4 00111001=>2 00111010=>2 00111011=>1 00111100=>3 00111101=>1 00111110=>2 00111111=>1 01000000=>7 01000001=>2 01000010=>3 01000011=>2 01000100=>4 01000101=>2 01000110=>3 01000111=>2 01001000=>5 01001001=>3 01001010=>3 01001011=>2 01001100=>4 01001101=>2 01001110=>3 01001111=>2 01010000=>6 01010001=>3 01010010=>4 01010011=>3 01010100=>5 01010101=>4 01010110=>2 01010111=>1 01011000=>4 01011001=>2 01011010=>3 01011011=>1 01011100=>3 01011101=>2 01011110=>2 01011111=>1 01100000=>6 01100001=>2 01100010=>3 01100011=>2 01100100=>4 01100101=>2 01100110=>3 01100111=>2 01101000=>5 01101001=>3 01101010=>4 01101011=>2 01101100=>4 01101101=>3 01101110=>2 01101111=>1 01110000=>5 01110001=>2 01110010=>3 01110011=>2 01110100=>4 01110101=>3 01110110=>3 01110111=>2 01111000=>4 01111001=>2 01111010=>3 01111011=>2 01111100=>3 01111101=>2 01111110=>2 01111111=>1 10000000=>8 10000001=>2 10000010=>3 10000011=>2 10000100=>4 10000101=>2 10000110=>3 10000111=>2 10001000=>5 10001001=>2 10001010=>3 10001011=>2 10001100=>4 10001101=>2 10001110=>3 10001111=>2 10010000=>6 10010001=>3 10010010=>4 10010011=>2 10010100=>4 10010101=>2 10010110=>3 10010111=>2 10011000=>5 10011001=>3 10011010=>3 10011011=>2 10011100=>4 10011101=>2 10011110=>3 10011111=>2 10100000=>7 10100001=>3 10100010=>4 10100011=>3 10100100=>5 10100101=>3 10100110=>4 10100111=>3 10101000=>6 10101001=>4 10101010=>5 10101011=>2 10101100=>4 10101101=>3 10101110=>3 10101111=>2 10110000=>6 10110001=>3 10110010=>4 10110011=>3 10110100=>5 10110101=>4 10110110=>4 10110111=>2 10111000=>5 10111001=>3 10111010=>4 10111011=>3 10111100=>4 10111101=>3 10111110=>3 10111111=>2 11000000=>8 11000001=>3 11000010=>4 11000011=>3 11000100=>5 11000101=>3 11000110=>4 11000111=>3 11001000=>6 11001001=>4 11001010=>4 11001011=>3 11001100=>5 11001101=>3 11001110=>4 11001111=>3 11010000=>7 11010001=>4 11010010=>5 11010011=>4 11010100=>6 11010101=>5 11010110=>4 11010111=>3 11011000=>6 11011001=>4 11011010=>5 11011011=>4 11011100=>5 11011101=>4 11011110=>4 11011111=>3 11100000=>8 11100001=>4 11100010=>5 11100011=>4 11100100=>6 11100101=>4 11100110=>5 11100111=>4 11101000=>7 11101001=>5 11101010=>6 11101011=>4 11101100=>6 11101101=>5 11101110=>5 11101111=>4 11110000=>8 11110001=>5 11110010=>6 11110011=>5 11110100=>7 11110101=>6 11110110=>6 11110111=>5 11111000=>8 11111001=>6 11111010=>7 11111011=>6 11111100=>8 11111101=>7 11111110=>8 11111111=>8 000000000=>9 000000001=>1 000000010=>2 000000011=>1 000000100=>3 000000101=>1 000000110=>2 000000111=>1 000001000=>4 000001001=>1 000001010=>2 000001011=>1 000001100=>3 000001101=>1 000001110=>2 000001111=>1 000010000=>5 000010001=>1 000010010=>2 000010011=>1 000010100=>3 000010101=>1 000010110=>2 000010111=>1 000011000=>4 000011001=>1 000011010=>2 000011011=>1 000011100=>3 000011101=>1 000011110=>2 000011111=>1 000100000=>6 000100001=>2 000100010=>3 000100011=>1 000100100=>3 000100101=>1 000100110=>2 000100111=>1 000101000=>4 000101001=>1 000101010=>2 000101011=>1 000101100=>3 000101101=>1 000101110=>2 000101111=>1 000110000=>5 000110001=>2 000110010=>2 000110011=>1 000110100=>3 000110101=>1 000110110=>2 000110111=>1 000111000=>4 000111001=>1 000111010=>2 000111011=>1 000111100=>3 000111101=>1 000111110=>2 000111111=>1 001000000=>7 001000001=>2 001000010=>3 001000011=>2 001000100=>4 001000101=>2 001000110=>3 001000111=>2 001001000=>5 001001001=>3 001001010=>2 001001011=>1 001001100=>3 001001101=>1 001001110=>2 001001111=>1 001010000=>5 001010001=>2 001010010=>3 001010011=>1 001010100=>3 001010101=>1 001010110=>2 001010111=>1 001011000=>4 001011001=>2 001011010=>2 001011011=>1 001011100=>3 001011101=>1 001011110=>2 001011111=>1 001100000=>6 001100001=>2 001100010=>3 001100011=>2 001100100=>4 001100101=>2 001100110=>3 001100111=>1 001101000=>4 001101001=>2 001101010=>2 001101011=>1 001101100=>3 001101101=>1 001101110=>2 001101111=>1 001110000=>5 001110001=>2 001110010=>3 001110011=>2 001110100=>3 001110101=>1 001110110=>2 001110111=>1 001111000=>4 001111001=>2 001111010=>2 001111011=>1 001111100=>3 001111101=>1 001111110=>2 001111111=>1 010000000=>8 010000001=>2 010000010=>3 010000011=>2 010000100=>4 010000101=>2 010000110=>3 010000111=>2 010001000=>5 010001001=>2 010001010=>3 010001011=>2 010001100=>4 010001101=>2 010001110=>3 010001111=>2 010010000=>6 010010001=>3 010010010=>4 010010011=>2 010010100=>4 010010101=>2 010010110=>3 010010111=>2 010011000=>5 010011001=>3 010011010=>3 010011011=>2 010011100=>4 010011101=>2 010011110=>3 010011111=>2 010100000=>7 010100001=>3 010100010=>4 010100011=>3 010100100=>5 010100101=>3 010100110=>4 010100111=>3 010101000=>6 010101001=>4 010101010=>5 010101011=>1 010101100=>3 010101101=>2 010101110=>2 010101111=>1 010110000=>5 010110001=>2 010110010=>3 010110011=>2 010110100=>4 010110101=>3 010110110=>2 010110111=>1 010111000=>4 010111001=>2 010111010=>3 010111011=>1 010111100=>3 010111101=>2 010111110=>2 010111111=>1 011000000=>7 011000001=>2 011000010=>3 011000011=>2 011000100=>4 011000101=>2 011000110=>3 011000111=>2 011001000=>5 011001001=>3 011001010=>3 011001011=>2 011001100=>4 011001101=>2 011001110=>3 011001111=>2 011010000=>6 011010001=>3 011010010=>4 011010011=>3 011010100=>5 011010101=>4 011010110=>3 011010111=>2 011011000=>5 011011001=>3 011011010=>4 011011011=>3 011011100=>3 011011101=>2 011011110=>2 011011111=>1 011100000=>6 011100001=>2 011100010=>3 011100011=>2 011100100=>4 011100101=>2 011100110=>3 011100111=>2 011101000=>5 011101001=>3 011101010=>4 011101011=>2 011101100=>4 011101101=>3 011101110=>3 011101111=>1 011110000=>5 011110001=>2 011110010=>3 011110011=>2 011110100=>4 011110101=>3 011110110=>3 011110111=>2 011111000=>4 011111001=>2 011111010=>3 011111011=>2 011111100=>3 011111101=>2 011111110=>2 011111111=>1 100000000=>9 100000001=>2 100000010=>3 100000011=>2 100000100=>4 100000101=>2 100000110=>3 100000111=>2 100001000=>5 100001001=>2 100001010=>3 100001011=>2 100001100=>4 100001101=>2 100001110=>3 100001111=>2 100010000=>6 100010001=>3 100010010=>3 100010011=>2 100010100=>4 100010101=>2 100010110=>3 100010111=>2 100011000=>5 100011001=>2 100011010=>3 100011011=>2 100011100=>4 100011101=>2 100011110=>3 100011111=>2 100100000=>7 100100001=>3 100100010=>4 100100011=>3 100100100=>5 100100101=>2 100100110=>3 100100111=>2 100101000=>5 100101001=>3 100101010=>3 100101011=>2 100101100=>4 100101101=>2 100101110=>3 100101111=>2 100110000=>6 100110001=>3 100110010=>4 100110011=>3 100110100=>4 100110101=>2 100110110=>3 100110111=>2 100111000=>5 100111001=>3 100111010=>3 100111011=>2 100111100=>4 100111101=>2 100111110=>3 100111111=>2 101000000=>8 101000001=>3 101000010=>4 101000011=>3 101000100=>5 101000101=>3 101000110=>4 101000111=>3 101001000=>6 101001001=>4 101001010=>4 101001011=>3 101001100=>5 101001101=>3 101001110=>4 101001111=>3 101010000=>7 101010001=>4 101010010=>5 101010011=>4 101010100=>6 101010101=>5 101010110=>3 101010111=>2 101011000=>5 101011001=>3 101011010=>4 101011011=>2 101011100=>4 101011101=>3 101011110=>3 101011111=>2 101100000=>7 101100001=>3 101100010=>4 101100011=>3 101100100=>5 101100101=>3 101100110=>4 101100111=>3 101101000=>6 101101001=>4 101101010=>5 101101011=>3 101101100=>5 101101101=>4 101101110=>3 101101111=>2 101110000=>6 101110001=>3 101110010=>4 101110011=>3 101110100=>5 101110101=>4 101110110=>4 101110111=>3 101111000=>5 101111001=>3 101111010=>4 101111011=>3 101111100=>4 101111101=>3 101111110=>3 101111111=>2 110000000=>9 110000001=>3 110000010=>4 110000011=>3 110000100=>5 110000101=>3 110000110=>4 110000111=>3 110001000=>6 110001001=>3 110001010=>4 110001011=>3 110001100=>5 110001101=>3 110001110=>4 110001111=>3 110010000=>7 110010001=>4 110010010=>5 110010011=>3 110010100=>5 110010101=>3 110010110=>4 110010111=>3 110011000=>6 110011001=>4 110011010=>4 110011011=>3 110011100=>5 110011101=>3 110011110=>4 110011111=>3 110100000=>8 110100001=>4 110100010=>5 110100011=>4 110100100=>6 110100101=>4 110100110=>5 110100111=>4 110101000=>7 110101001=>5 110101010=>6 110101011=>3 110101100=>5 110101101=>4 110101110=>4 110101111=>3 110110000=>7 110110001=>4 110110010=>5 110110011=>4 110110100=>6 110110101=>5 110110110=>5 110110111=>3 110111000=>6 110111001=>4 110111010=>5 110111011=>4 110111100=>5 110111101=>4 110111110=>4 110111111=>3 111000000=>9 111000001=>4 111000010=>5 111000011=>4 111000100=>6 111000101=>4 111000110=>5 111000111=>4 111001000=>7 111001001=>5 111001010=>5 111001011=>4 111001100=>6 111001101=>4 111001110=>5 111001111=>4 111010000=>8 111010001=>5 111010010=>6 111010011=>5 111010100=>7 111010101=>6 111010110=>5 111010111=>4 111011000=>7 111011001=>5 111011010=>6 111011011=>5 111011100=>6 111011101=>5 111011110=>5 111011111=>4 111100000=>9 111100001=>5 111100010=>6 111100011=>5 111100100=>7 111100101=>5 111100110=>6 111100111=>5 111101000=>8 111101001=>6 111101010=>7 111101011=>5 111101100=>7 111101101=>6 111101110=>6 111101111=>5 111110000=>9 111110001=>6 111110010=>7 111110011=>6 111110100=>8 111110101=>7 111110110=>7 111110111=>6 111111000=>9 111111001=>7 111111010=>8 111111011=>7 111111100=>9 111111101=>8 111111110=>9 111111111=>9
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Description
The length of the Lyndon factorization of the binary word.
The Lyndon factorization of a finite word w is its unique factorization as a non-increasing product of Lyndon words, i.e., $w = l_1\dots l_n$ where each $l_i$ is a Lyndon word and $l_1 \geq\dots\geq l_n$.
References
[1] wikipedia:Lyndon word
[2] Duval, J.-P. Factorizing words over an ordered alphabet MathSciNet:0729232
Code
def statistic(w):
    return len(w.lyndon_factorization())

Created
Oct 05, 2018 at 09:42 by Martin Rubey
Updated
Oct 05, 2018 at 09:42 by Martin Rubey