Identifier
- St001267: Binary words ⟶ ℤ
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 $l_1 \geq\dots\geq l_n$.
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
[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
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