Identifier
-
Mp00261:
Binary words
—Burrows-Wheeler⟶
Binary words
St000291: Binary words ⟶ ℤ
Values
0 => 0 => 0
1 => 1 => 0
00 => 00 => 0
01 => 10 => 1
10 => 10 => 1
11 => 11 => 0
000 => 000 => 0
001 => 100 => 1
010 => 100 => 1
011 => 110 => 1
100 => 100 => 1
101 => 110 => 1
110 => 110 => 1
111 => 111 => 0
0000 => 0000 => 0
0001 => 1000 => 1
0010 => 1000 => 1
0011 => 1010 => 2
0100 => 1000 => 1
0101 => 1100 => 1
0110 => 1010 => 2
0111 => 1110 => 1
1000 => 1000 => 1
1001 => 1010 => 2
1010 => 1100 => 1
1011 => 1110 => 1
1100 => 1010 => 2
1101 => 1110 => 1
1110 => 1110 => 1
1111 => 1111 => 0
00000 => 00000 => 0
00001 => 10000 => 1
00010 => 10000 => 1
00011 => 10010 => 2
00100 => 10000 => 1
00101 => 11000 => 1
00110 => 10010 => 2
00111 => 10110 => 2
01000 => 10000 => 1
01001 => 11000 => 1
01010 => 11000 => 1
01011 => 11100 => 1
01100 => 10010 => 2
01101 => 11100 => 1
01110 => 10110 => 2
01111 => 11110 => 1
10000 => 10000 => 1
10001 => 10010 => 2
10010 => 11000 => 1
10011 => 10110 => 2
10100 => 11000 => 1
10101 => 11100 => 1
10110 => 11100 => 1
10111 => 11110 => 1
11000 => 10010 => 2
11001 => 10110 => 2
11010 => 11100 => 1
11011 => 11110 => 1
11100 => 10110 => 2
11101 => 11110 => 1
11110 => 11110 => 1
11111 => 11111 => 0
000000 => 000000 => 0
000001 => 100000 => 1
000010 => 100000 => 1
000011 => 100010 => 2
000100 => 100000 => 1
000101 => 101000 => 2
000110 => 100010 => 2
000111 => 100110 => 2
001000 => 100000 => 1
001001 => 110000 => 1
001010 => 101000 => 2
001011 => 101100 => 2
001100 => 100010 => 2
001101 => 110010 => 2
001110 => 100110 => 2
001111 => 101110 => 2
010000 => 100000 => 1
010001 => 101000 => 2
010010 => 110000 => 1
010011 => 110010 => 2
010100 => 101000 => 2
010101 => 111000 => 1
010110 => 101100 => 2
010111 => 111010 => 2
011000 => 100010 => 2
011001 => 101100 => 2
011010 => 110010 => 2
011011 => 111100 => 1
011100 => 100110 => 2
011101 => 111010 => 2
011110 => 101110 => 2
011111 => 111110 => 1
100000 => 100000 => 1
100001 => 100010 => 2
100010 => 101000 => 2
100011 => 100110 => 2
100100 => 110000 => 1
100101 => 101100 => 2
100110 => 110010 => 2
>>> Load all 1289 entries. <<<100111 => 101110 => 2
101000 => 101000 => 2
101001 => 110010 => 2
101010 => 111000 => 1
101011 => 111010 => 2
101100 => 101100 => 2
101101 => 111100 => 1
101110 => 111010 => 2
101111 => 111110 => 1
110000 => 100010 => 2
110001 => 100110 => 2
110010 => 101100 => 2
110011 => 101110 => 2
110100 => 110010 => 2
110101 => 111010 => 2
110110 => 111100 => 1
110111 => 111110 => 1
111000 => 100110 => 2
111001 => 101110 => 2
111010 => 111010 => 2
111011 => 111110 => 1
111100 => 101110 => 2
111101 => 111110 => 1
111110 => 111110 => 1
111111 => 111111 => 0
0000000 => 0000000 => 0
0000001 => 1000000 => 1
0000010 => 1000000 => 1
0000011 => 1000010 => 2
0000100 => 1000000 => 1
0000101 => 1001000 => 2
0000110 => 1000010 => 2
0000111 => 1000110 => 2
0001000 => 1000000 => 1
0001001 => 1100000 => 1
0001010 => 1001000 => 2
0001011 => 1001100 => 2
0001100 => 1000010 => 2
0001101 => 1010010 => 3
0001110 => 1000110 => 2
0001111 => 1001110 => 2
0010000 => 1000000 => 1
0010001 => 1100000 => 1
0010010 => 1100000 => 1
0010011 => 1100100 => 2
0010100 => 1001000 => 2
0010101 => 1110000 => 1
0010110 => 1001100 => 2
0010111 => 1011010 => 3
0011000 => 1000010 => 2
0011001 => 1100100 => 2
0011010 => 1010010 => 3
0011011 => 1101100 => 2
0011100 => 1000110 => 2
0011101 => 1100110 => 2
0011110 => 1001110 => 2
0011111 => 1011110 => 2
0100000 => 1000000 => 1
0100001 => 1001000 => 2
0100010 => 1100000 => 1
0100011 => 1010010 => 3
0100100 => 1100000 => 1
0100101 => 1110000 => 1
0100110 => 1100100 => 2
0100111 => 1100110 => 2
0101000 => 1001000 => 2
0101001 => 1110000 => 1
0101010 => 1110000 => 1
0101011 => 1111000 => 1
0101100 => 1001100 => 2
0101101 => 1111000 => 1
0101110 => 1011010 => 3
0101111 => 1110110 => 2
0110000 => 1000010 => 2
0110001 => 1001100 => 2
0110010 => 1100100 => 2
0110011 => 1101100 => 2
0110100 => 1010010 => 3
0110101 => 1111000 => 1
0110110 => 1101100 => 2
0110111 => 1111100 => 1
0111000 => 1000110 => 2
0111001 => 1011010 => 3
0111010 => 1100110 => 2
0111011 => 1111100 => 1
0111100 => 1001110 => 2
0111101 => 1110110 => 2
0111110 => 1011110 => 2
0111111 => 1111110 => 1
1000000 => 1000000 => 1
1000001 => 1000010 => 2
1000010 => 1001000 => 2
1000011 => 1000110 => 2
1000100 => 1100000 => 1
1000101 => 1001100 => 2
1000110 => 1010010 => 3
1000111 => 1001110 => 2
1001000 => 1100000 => 1
1001001 => 1100100 => 2
1001010 => 1110000 => 1
1001011 => 1011010 => 3
1001100 => 1100100 => 2
1001101 => 1101100 => 2
1001110 => 1100110 => 2
1001111 => 1011110 => 2
1010000 => 1001000 => 2
1010001 => 1010010 => 3
1010010 => 1110000 => 1
1010011 => 1100110 => 2
1010100 => 1110000 => 1
1010101 => 1111000 => 1
1010110 => 1111000 => 1
1010111 => 1110110 => 2
1011000 => 1001100 => 2
1011001 => 1101100 => 2
1011010 => 1111000 => 1
1011011 => 1111100 => 1
1011100 => 1011010 => 3
1011101 => 1111100 => 1
1011110 => 1110110 => 2
1011111 => 1111110 => 1
1100000 => 1000010 => 2
1100001 => 1000110 => 2
1100010 => 1001100 => 2
1100011 => 1001110 => 2
1100100 => 1100100 => 2
1100101 => 1011010 => 3
1100110 => 1101100 => 2
1100111 => 1011110 => 2
1101000 => 1010010 => 3
1101001 => 1100110 => 2
1101010 => 1111000 => 1
1101011 => 1110110 => 2
1101100 => 1101100 => 2
1101101 => 1111100 => 1
1101110 => 1111100 => 1
1101111 => 1111110 => 1
1110000 => 1000110 => 2
1110001 => 1001110 => 2
1110010 => 1011010 => 3
1110011 => 1011110 => 2
1110100 => 1100110 => 2
1110101 => 1110110 => 2
1110110 => 1111100 => 1
1110111 => 1111110 => 1
1111000 => 1001110 => 2
1111001 => 1011110 => 2
1111010 => 1110110 => 2
1111011 => 1111110 => 1
1111100 => 1011110 => 2
1111101 => 1111110 => 1
1111110 => 1111110 => 1
1111111 => 1111111 => 0
00000000 => 00000000 => 0
00000001 => 10000000 => 1
00000010 => 10000000 => 1
00000011 => 10000010 => 2
00000100 => 10000000 => 1
00000101 => 10001000 => 2
00000110 => 10000010 => 2
00000111 => 10000110 => 2
00001000 => 10000000 => 1
00001001 => 10100000 => 2
00001010 => 10001000 => 2
00001011 => 10001100 => 2
00001100 => 10000010 => 2
00001101 => 10010010 => 3
00001110 => 10000110 => 2
00001111 => 10001110 => 2
00010000 => 10000000 => 1
00010001 => 11000000 => 1
00010010 => 10100000 => 2
00010011 => 10100100 => 3
00010100 => 10001000 => 2
00010101 => 10110000 => 2
00010110 => 10001100 => 2
00010111 => 10011010 => 3
00011000 => 10000010 => 2
00011001 => 11000010 => 2
00011010 => 10010010 => 3
00011011 => 10101100 => 3
00011100 => 10000110 => 2
00011101 => 10100110 => 3
00011110 => 10001110 => 2
00011111 => 10011110 => 2
00100000 => 10000000 => 1
00100001 => 10100000 => 2
00100010 => 11000000 => 1
00100011 => 11000010 => 2
00100100 => 10100000 => 2
00100101 => 11100000 => 1
00100110 => 10100100 => 3
00100111 => 11001010 => 3
00101000 => 10001000 => 2
00101001 => 11100000 => 1
00101010 => 10110000 => 2
00101011 => 10111000 => 2
00101100 => 10001100 => 2
00101101 => 11010100 => 3
00101110 => 10011010 => 3
00101111 => 10110110 => 3
00110000 => 10000010 => 2
00110001 => 10100100 => 3
00110010 => 11000010 => 2
00110011 => 11001100 => 2
00110100 => 10010010 => 3
00110101 => 11100010 => 2
00110110 => 10101100 => 3
00110111 => 10111100 => 2
00111000 => 10000110 => 2
00111001 => 11001010 => 3
00111010 => 10100110 => 3
00111011 => 11011010 => 3
00111100 => 10001110 => 2
00111101 => 11001110 => 2
00111110 => 10011110 => 2
00111111 => 10111110 => 2
01000000 => 10000000 => 1
01000001 => 10001000 => 2
01000010 => 10100000 => 2
01000011 => 10010010 => 3
01000100 => 11000000 => 1
01000101 => 10110000 => 2
01000110 => 11000010 => 2
01000111 => 10100110 => 3
01001000 => 10100000 => 2
01001001 => 11100000 => 1
01001010 => 11100000 => 1
01001011 => 11010100 => 3
01001100 => 10100100 => 3
01001101 => 11100010 => 2
01001110 => 11001010 => 3
01001111 => 11001110 => 2
01010000 => 10001000 => 2
01010001 => 10110000 => 2
01010010 => 11100000 => 1
01010011 => 11100010 => 2
01010100 => 10110000 => 2
01010101 => 11110000 => 1
01010110 => 10111000 => 2
01010111 => 11110010 => 2
01011000 => 10001100 => 2
01011001 => 10111000 => 2
01011010 => 11010100 => 3
01011011 => 11111000 => 1
01011100 => 10011010 => 3
01011101 => 11110010 => 2
01011110 => 10110110 => 3
01011111 => 11101110 => 2
01100000 => 10000010 => 2
01100001 => 10001100 => 2
01100010 => 10100100 => 3
01100011 => 10101100 => 3
01100100 => 11000010 => 2
01100101 => 10111000 => 2
01100110 => 11001100 => 2
01100111 => 11011010 => 3
01101000 => 10010010 => 3
01101001 => 11010100 => 3
01101010 => 11100010 => 2
01101011 => 11111000 => 1
01101100 => 10101100 => 3
01101101 => 11111000 => 1
01101110 => 10111100 => 2
01101111 => 11111010 => 2
01110000 => 10000110 => 2
01110001 => 10011010 => 3
01110010 => 11001010 => 3
01110011 => 10111100 => 2
01110100 => 10100110 => 3
01110101 => 11110010 => 2
01110110 => 11011010 => 3
01110111 => 11111100 => 1
01111000 => 10001110 => 2
01111001 => 10110110 => 3
01111010 => 11001110 => 2
01111011 => 11111010 => 2
01111100 => 10011110 => 2
01111101 => 11101110 => 2
01111110 => 10111110 => 2
01111111 => 11111110 => 1
10000000 => 10000000 => 1
10000001 => 10000010 => 2
10000010 => 10001000 => 2
10000011 => 10000110 => 2
10000100 => 10100000 => 2
10000101 => 10001100 => 2
10000110 => 10010010 => 3
10000111 => 10001110 => 2
10001000 => 11000000 => 1
10001001 => 10100100 => 3
10001010 => 10110000 => 2
10001011 => 10011010 => 3
10001100 => 11000010 => 2
10001101 => 10101100 => 3
10001110 => 10100110 => 3
10001111 => 10011110 => 2
10010000 => 10100000 => 2
10010001 => 11000010 => 2
10010010 => 11100000 => 1
10010011 => 11001010 => 3
10010100 => 11100000 => 1
10010101 => 10111000 => 2
10010110 => 11010100 => 3
10010111 => 10110110 => 3
10011000 => 10100100 => 3
10011001 => 11001100 => 2
10011010 => 11100010 => 2
10011011 => 10111100 => 2
10011100 => 11001010 => 3
10011101 => 11011010 => 3
10011110 => 11001110 => 2
10011111 => 10111110 => 2
10100000 => 10001000 => 2
10100001 => 10010010 => 3
10100010 => 10110000 => 2
10100011 => 10100110 => 3
10100100 => 11100000 => 1
10100101 => 11010100 => 3
10100110 => 11100010 => 2
10100111 => 11001110 => 2
10101000 => 10110000 => 2
10101001 => 11100010 => 2
10101010 => 11110000 => 1
10101011 => 11110010 => 2
10101100 => 10111000 => 2
10101101 => 11111000 => 1
10101110 => 11110010 => 2
10101111 => 11101110 => 2
10110000 => 10001100 => 2
10110001 => 10101100 => 3
10110010 => 10111000 => 2
10110011 => 11011010 => 3
10110100 => 11010100 => 3
10110101 => 11111000 => 1
10110110 => 11111000 => 1
10110111 => 11111010 => 2
10111000 => 10011010 => 3
10111001 => 10111100 => 2
10111010 => 11110010 => 2
10111011 => 11111100 => 1
10111100 => 10110110 => 3
10111101 => 11111010 => 2
10111110 => 11101110 => 2
10111111 => 11111110 => 1
11000000 => 10000010 => 2
11000001 => 10000110 => 2
11000010 => 10001100 => 2
11000011 => 10001110 => 2
11000100 => 10100100 => 3
11000101 => 10011010 => 3
11000110 => 10101100 => 3
11000111 => 10011110 => 2
11001000 => 11000010 => 2
11001001 => 11001010 => 3
11001010 => 10111000 => 2
11001011 => 10110110 => 3
11001100 => 11001100 => 2
11001101 => 10111100 => 2
11001110 => 11011010 => 3
11001111 => 10111110 => 2
11010000 => 10010010 => 3
11010001 => 10100110 => 3
11010010 => 11010100 => 3
11010011 => 11001110 => 2
11010100 => 11100010 => 2
11010101 => 11110010 => 2
11010110 => 11111000 => 1
11010111 => 11101110 => 2
11011000 => 10101100 => 3
11011001 => 11011010 => 3
11011010 => 11111000 => 1
11011011 => 11111010 => 2
11011100 => 10111100 => 2
11011101 => 11111100 => 1
11011110 => 11111010 => 2
11011111 => 11111110 => 1
11100000 => 10000110 => 2
11100001 => 10001110 => 2
11100010 => 10011010 => 3
11100011 => 10011110 => 2
11100100 => 11001010 => 3
11100101 => 10110110 => 3
11100110 => 10111100 => 2
11100111 => 10111110 => 2
11101000 => 10100110 => 3
11101001 => 11001110 => 2
11101010 => 11110010 => 2
11101011 => 11101110 => 2
11101100 => 11011010 => 3
11101101 => 11111010 => 2
11101110 => 11111100 => 1
11101111 => 11111110 => 1
11110000 => 10001110 => 2
11110001 => 10011110 => 2
11110010 => 10110110 => 3
11110011 => 10111110 => 2
11110100 => 11001110 => 2
11110101 => 11101110 => 2
11110110 => 11111010 => 2
11110111 => 11111110 => 1
11111000 => 10011110 => 2
11111001 => 10111110 => 2
11111010 => 11101110 => 2
11111011 => 11111110 => 1
11111100 => 10111110 => 2
11111101 => 11111110 => 1
11111110 => 11111110 => 1
11111111 => 11111111 => 0
000000000 => 000000000 => 0
000000001 => 100000000 => 1
000000010 => 100000000 => 1
000000011 => 100000010 => 2
000000100 => 100000000 => 1
000000101 => 100001000 => 2
000000110 => 100000010 => 2
000000111 => 100000110 => 2
000001000 => 100000000 => 1
000001001 => 100100000 => 2
000001010 => 100001000 => 2
000001011 => 100001100 => 2
000001100 => 100000010 => 2
000001101 => 100010010 => 3
000001110 => 100000110 => 2
000001111 => 100001110 => 2
000010000 => 100000000 => 1
000010001 => 110000000 => 1
000010010 => 100100000 => 2
000010011 => 100100100 => 3
000010100 => 100001000 => 2
000010101 => 100110000 => 2
000010110 => 100001100 => 2
000010111 => 100011010 => 3
000011000 => 100000010 => 2
000011001 => 101000010 => 3
000011010 => 100010010 => 3
000011011 => 100101100 => 3
000011100 => 100000110 => 2
000011101 => 100100110 => 3
000011110 => 100001110 => 2
000011111 => 100011110 => 2
000100000 => 100000000 => 1
000100001 => 110000000 => 1
000100010 => 110000000 => 1
000100011 => 110000100 => 2
000100100 => 100100000 => 2
000100101 => 101100000 => 2
000100110 => 100100100 => 3
000100111 => 101001010 => 4
000101000 => 100001000 => 2
000101001 => 110010000 => 2
000101010 => 100110000 => 2
000101011 => 100111000 => 2
000101100 => 100001100 => 2
000101101 => 101010100 => 4
000101110 => 100011010 => 3
000101111 => 100110110 => 3
000110000 => 100000010 => 2
000110001 => 110000100 => 2
000110010 => 101000010 => 3
000110011 => 110001100 => 2
000110100 => 100010010 => 3
000110101 => 101100010 => 3
000110110 => 100101100 => 3
000110111 => 100111100 => 2
000111000 => 100000110 => 2
000111001 => 110000110 => 2
000111010 => 100100110 => 3
000111011 => 101011010 => 4
000111100 => 100001110 => 2
000111101 => 101001110 => 3
000111110 => 100011110 => 2
000111111 => 100111110 => 2
001000000 => 100000000 => 1
001000001 => 100100000 => 2
001000010 => 110000000 => 1
001000011 => 101000010 => 3
001000100 => 110000000 => 1
001000101 => 110010000 => 2
001000110 => 110000100 => 2
001000111 => 110000110 => 2
001001000 => 100100000 => 2
001001001 => 111000000 => 1
001001010 => 101100000 => 2
001001011 => 110011000 => 2
001001100 => 100100100 => 3
001001101 => 111000010 => 2
001001110 => 101001010 => 4
001001111 => 110010110 => 3
001010000 => 100001000 => 2
001010001 => 101100000 => 2
001010010 => 110010000 => 2
001010011 => 111001000 => 2
001010100 => 100110000 => 2
001010101 => 111100000 => 1
001010110 => 100111000 => 2
001010111 => 101110010 => 3
001011000 => 100001100 => 2
001011001 => 110011000 => 2
001011010 => 101010100 => 4
001011011 => 101111000 => 2
001011100 => 100011010 => 3
001011101 => 110101010 => 4
001011110 => 100110110 => 3
001011111 => 101101110 => 3
001100000 => 100000010 => 2
001100001 => 100100100 => 3
001100010 => 110000100 => 2
001100011 => 110001100 => 2
001100100 => 101000010 => 3
001100101 => 111001000 => 2
001100110 => 110001100 => 2
001100111 => 110011100 => 2
001101000 => 100010010 => 3
001101001 => 111000010 => 2
001101010 => 101100010 => 3
001101011 => 111011000 => 2
001101100 => 100101100 => 3
001101101 => 111001100 => 2
001101110 => 100111100 => 2
001101111 => 101111010 => 3
001110000 => 100000110 => 2
001110001 => 101001010 => 4
001110010 => 110000110 => 2
001110011 => 110011100 => 2
001110100 => 100100110 => 3
001110101 => 111000110 => 2
001110110 => 101011010 => 4
001110111 => 110111100 => 2
001111000 => 100001110 => 2
001111001 => 110010110 => 3
001111010 => 101001110 => 3
001111011 => 110110110 => 3
001111100 => 100011110 => 2
001111101 => 110011110 => 2
001111110 => 100111110 => 2
001111111 => 101111110 => 2
010000000 => 100000000 => 1
010000001 => 100001000 => 2
010000010 => 100100000 => 2
010000011 => 100010010 => 3
010000100 => 110000000 => 1
010000101 => 100110000 => 2
010000110 => 101000010 => 3
010000111 => 100100110 => 3
010001000 => 110000000 => 1
010001001 => 101100000 => 2
010001010 => 110010000 => 2
010001011 => 101010100 => 4
010001100 => 110000100 => 2
010001101 => 101100010 => 3
010001110 => 110000110 => 2
010001111 => 101001110 => 3
010010000 => 100100000 => 2
010010001 => 110010000 => 2
010010010 => 111000000 => 1
010010011 => 111000010 => 2
010010100 => 101100000 => 2
010010101 => 111100000 => 1
010010110 => 110011000 => 2
010010111 => 110101010 => 4
010011000 => 100100100 => 3
010011001 => 111001000 => 2
010011010 => 111000010 => 2
010011011 => 111001100 => 2
010011100 => 101001010 => 4
010011101 => 111000110 => 2
010011110 => 110010110 => 3
010011111 => 110011110 => 2
010100000 => 100001000 => 2
010100001 => 100110000 => 2
010100010 => 101100000 => 2
010100011 => 101100010 => 3
010100100 => 110010000 => 2
010100101 => 111100000 => 1
010100110 => 111001000 => 2
010100111 => 111000110 => 2
010101000 => 100110000 => 2
010101001 => 111100000 => 1
010101010 => 111100000 => 1
010101011 => 111110000 => 1
010101100 => 100111000 => 2
010101101 => 111110000 => 1
010101110 => 101110010 => 3
010101111 => 111100110 => 2
010110000 => 100001100 => 2
010110001 => 100111000 => 2
010110010 => 110011000 => 2
010110011 => 111011000 => 2
010110100 => 101010100 => 4
010110101 => 111110000 => 1
010110110 => 101111000 => 2
010110111 => 111101100 => 2
010111000 => 100011010 => 3
010111001 => 101110010 => 3
010111010 => 110101010 => 4
010111011 => 111110010 => 2
010111100 => 100110110 => 3
010111101 => 111100110 => 2
010111110 => 101101110 => 3
010111111 => 111011110 => 2
011000000 => 100000010 => 2
011000001 => 100001100 => 2
011000010 => 100100100 => 3
011000011 => 100101100 => 3
011000100 => 110000100 => 2
011000101 => 100111000 => 2
011000110 => 110001100 => 2
011000111 => 101011010 => 4
011001000 => 101000010 => 3
011001001 => 110011000 => 2
011001010 => 111001000 => 2
011001011 => 101111000 => 2
011001100 => 110001100 => 2
011001101 => 111011000 => 2
011001110 => 110011100 => 2
011001111 => 110110110 => 3
011010000 => 100010010 => 3
011010001 => 101010100 => 4
011010010 => 111000010 => 2
011010011 => 111001100 => 2
011010100 => 101100010 => 3
011010101 => 111110000 => 1
011010110 => 111011000 => 2
011010111 => 111110010 => 2
011011000 => 100101100 => 3
011011001 => 101111000 => 2
011011010 => 111001100 => 2
011011011 => 111111000 => 1
011011100 => 100111100 => 2
011011101 => 111101100 => 2
011011110 => 101111010 => 3
011011111 => 111110110 => 2
011100000 => 100000110 => 2
011100001 => 100011010 => 3
011100010 => 101001010 => 4
011100011 => 100111100 => 2
011100100 => 110000110 => 2
011100101 => 101110010 => 3
011100110 => 110011100 => 2
011100111 => 110111100 => 2
011101000 => 100100110 => 3
011101001 => 110101010 => 4
011101010 => 111000110 => 2
011101011 => 111101100 => 2
011101100 => 101011010 => 4
011101101 => 111110010 => 2
011101110 => 110111100 => 2
011101111 => 111111100 => 1
011110000 => 100001110 => 2
011110001 => 100110110 => 3
011110010 => 110010110 => 3
011110011 => 101111010 => 3
011110100 => 101001110 => 3
011110101 => 111100110 => 2
011110110 => 110110110 => 3
011110111 => 111111100 => 1
011111000 => 100011110 => 2
011111001 => 101101110 => 3
011111010 => 110011110 => 2
011111011 => 111110110 => 2
011111100 => 100111110 => 2
011111101 => 111011110 => 2
011111110 => 101111110 => 2
011111111 => 111111110 => 1
100000000 => 100000000 => 1
100000001 => 100000010 => 2
100000010 => 100001000 => 2
100000011 => 100000110 => 2
100000100 => 100100000 => 2
100000101 => 100001100 => 2
100000110 => 100010010 => 3
100000111 => 100001110 => 2
100001000 => 110000000 => 1
100001001 => 100100100 => 3
100001010 => 100110000 => 2
100001011 => 100011010 => 3
100001100 => 101000010 => 3
100001101 => 100101100 => 3
100001110 => 100100110 => 3
100001111 => 100011110 => 2
100010000 => 110000000 => 1
100010001 => 110000100 => 2
100010010 => 101100000 => 2
100010011 => 101001010 => 4
100010100 => 110010000 => 2
100010101 => 100111000 => 2
100010110 => 101010100 => 4
100010111 => 100110110 => 3
100011000 => 110000100 => 2
100011001 => 110001100 => 2
100011010 => 101100010 => 3
100011011 => 100111100 => 2
100011100 => 110000110 => 2
100011101 => 101011010 => 4
100011110 => 101001110 => 3
100011111 => 100111110 => 2
100100000 => 100100000 => 2
100100001 => 101000010 => 3
100100010 => 110010000 => 2
100100011 => 110000110 => 2
100100100 => 111000000 => 1
100100101 => 110011000 => 2
100100110 => 111000010 => 2
100100111 => 110010110 => 3
100101000 => 101100000 => 2
100101001 => 111001000 => 2
100101010 => 111100000 => 1
100101011 => 101110010 => 3
100101100 => 110011000 => 2
100101101 => 101111000 => 2
100101110 => 110101010 => 4
100101111 => 101101110 => 3
100110000 => 100100100 => 3
100110001 => 110001100 => 2
100110010 => 111001000 => 2
100110011 => 110011100 => 2
100110100 => 111000010 => 2
100110101 => 111011000 => 2
100110110 => 111001100 => 2
100110111 => 101111010 => 3
100111000 => 101001010 => 4
100111001 => 110011100 => 2
100111010 => 111000110 => 2
100111011 => 110111100 => 2
100111100 => 110010110 => 3
100111101 => 110110110 => 3
100111110 => 110011110 => 2
100111111 => 101111110 => 2
101000000 => 100001000 => 2
101000001 => 100010010 => 3
101000010 => 100110000 => 2
101000011 => 100100110 => 3
101000100 => 101100000 => 2
101000101 => 101010100 => 4
101000110 => 101100010 => 3
101000111 => 101001110 => 3
101001000 => 110010000 => 2
101001001 => 111000010 => 2
101001010 => 111100000 => 1
101001011 => 110101010 => 4
101001100 => 111001000 => 2
101001101 => 111001100 => 2
101001110 => 111000110 => 2
101001111 => 110011110 => 2
101010000 => 100110000 => 2
101010001 => 101100010 => 3
101010010 => 111100000 => 1
101010011 => 111000110 => 2
101010100 => 111100000 => 1
101010101 => 111110000 => 1
101010110 => 111110000 => 1
101010111 => 111100110 => 2
101011000 => 100111000 => 2
101011001 => 111011000 => 2
101011010 => 111110000 => 1
101011011 => 111101100 => 2
101011100 => 101110010 => 3
101011101 => 111110010 => 2
101011110 => 111100110 => 2
101011111 => 111011110 => 2
101100000 => 100001100 => 2
101100001 => 100101100 => 3
101100010 => 100111000 => 2
101100011 => 101011010 => 4
101100100 => 110011000 => 2
101100101 => 101111000 => 2
101100110 => 111011000 => 2
101100111 => 110110110 => 3
101101000 => 101010100 => 4
101101001 => 111001100 => 2
101101010 => 111110000 => 1
101101011 => 111110010 => 2
101101100 => 101111000 => 2
101101101 => 111111000 => 1
101101110 => 111101100 => 2
101101111 => 111110110 => 2
101110000 => 100011010 => 3
101110001 => 100111100 => 2
101110010 => 101110010 => 3
101110011 => 110111100 => 2
101110100 => 110101010 => 4
101110101 => 111101100 => 2
101110110 => 111110010 => 2
101110111 => 111111100 => 1
101111000 => 100110110 => 3
101111001 => 101111010 => 3
101111010 => 111100110 => 2
101111011 => 111111100 => 1
101111100 => 101101110 => 3
101111101 => 111110110 => 2
101111110 => 111011110 => 2
101111111 => 111111110 => 1
110000000 => 100000010 => 2
110000001 => 100000110 => 2
110000010 => 100001100 => 2
110000011 => 100001110 => 2
110000100 => 100100100 => 3
110000101 => 100011010 => 3
110000110 => 100101100 => 3
110000111 => 100011110 => 2
110001000 => 110000100 => 2
110001001 => 101001010 => 4
110001010 => 100111000 => 2
110001011 => 100110110 => 3
110001100 => 110001100 => 2
110001101 => 100111100 => 2
110001110 => 101011010 => 4
110001111 => 100111110 => 2
110010000 => 101000010 => 3
110010001 => 110000110 => 2
110010010 => 110011000 => 2
110010011 => 110010110 => 3
110010100 => 111001000 => 2
110010101 => 101110010 => 3
110010110 => 101111000 => 2
110010111 => 101101110 => 3
110011000 => 110001100 => 2
110011001 => 110011100 => 2
110011010 => 111011000 => 2
110011011 => 101111010 => 3
110011100 => 110011100 => 2
110011101 => 110111100 => 2
110011110 => 110110110 => 3
110011111 => 101111110 => 2
110100000 => 100010010 => 3
110100001 => 100100110 => 3
110100010 => 101010100 => 4
110100011 => 101001110 => 3
110100100 => 111000010 => 2
110100101 => 110101010 => 4
110100110 => 111001100 => 2
110100111 => 110011110 => 2
110101000 => 101100010 => 3
110101001 => 111000110 => 2
110101010 => 111110000 => 1
110101011 => 111100110 => 2
110101100 => 111011000 => 2
110101101 => 111101100 => 2
110101110 => 111110010 => 2
110101111 => 111011110 => 2
110110000 => 100101100 => 3
110110001 => 101011010 => 4
110110010 => 101111000 => 2
110110011 => 110110110 => 3
110110100 => 111001100 => 2
110110101 => 111110010 => 2
110110110 => 111111000 => 1
110110111 => 111110110 => 2
110111000 => 100111100 => 2
110111001 => 110111100 => 2
110111010 => 111101100 => 2
110111011 => 111111100 => 1
110111100 => 101111010 => 3
110111101 => 111111100 => 1
110111110 => 111110110 => 2
110111111 => 111111110 => 1
111000000 => 100000110 => 2
111000001 => 100001110 => 2
111000010 => 100011010 => 3
111000011 => 100011110 => 2
111000100 => 101001010 => 4
111000101 => 100110110 => 3
111000110 => 100111100 => 2
111000111 => 100111110 => 2
111001000 => 110000110 => 2
111001001 => 110010110 => 3
111001010 => 101110010 => 3
111001011 => 101101110 => 3
111001100 => 110011100 => 2
111001101 => 101111010 => 3
111001110 => 110111100 => 2
111001111 => 101111110 => 2
111010000 => 100100110 => 3
111010001 => 101001110 => 3
111010010 => 110101010 => 4
111010011 => 110011110 => 2
111010100 => 111000110 => 2
111010101 => 111100110 => 2
111010110 => 111101100 => 2
111010111 => 111011110 => 2
111011000 => 101011010 => 4
111011001 => 110110110 => 3
111011010 => 111110010 => 2
111011011 => 111110110 => 2
111011100 => 110111100 => 2
111011101 => 111111100 => 1
111011110 => 111111100 => 1
111011111 => 111111110 => 1
111100000 => 100001110 => 2
111100001 => 100011110 => 2
111100010 => 100110110 => 3
111100011 => 100111110 => 2
111100100 => 110010110 => 3
111100101 => 101101110 => 3
111100110 => 101111010 => 3
111100111 => 101111110 => 2
111101000 => 101001110 => 3
111101001 => 110011110 => 2
111101010 => 111100110 => 2
111101011 => 111011110 => 2
111101100 => 110110110 => 3
111101101 => 111110110 => 2
111101110 => 111111100 => 1
111101111 => 111111110 => 1
111110000 => 100011110 => 2
111110001 => 100111110 => 2
111110010 => 101101110 => 3
111110011 => 101111110 => 2
111110100 => 110011110 => 2
111110101 => 111011110 => 2
111110110 => 111110110 => 2
111110111 => 111111110 => 1
111111000 => 100111110 => 2
111111001 => 101111110 => 2
111111010 => 111011110 => 2
111111011 => 111111110 => 1
111111100 => 101111110 => 2
111111101 => 111111110 => 1
111111110 => 111111110 => 1
111111111 => 111111111 => 0
1010101010 => 1111100000 => 1
1010101100 => 1011110000 => 2
1010110010 => 1011110000 => 2
1010110100 => 1101101000 => 3
1011001010 => 1011110000 => 2
1011001100 => 1100111000 => 2
1011010010 => 1101101000 => 3
1011010100 => 1110100100 => 3
1011011000 => 1001111000 => 2
1011100100 => 1100110010 => 3
1011101000 => 1010101010 => 5
1011110000 => 1000110110 => 3
1100101010 => 1011110000 => 2
1100101100 => 1100111000 => 2
1100110010 => 1100111000 => 2
1100110100 => 1110001100 => 2
1101001010 => 1101101000 => 3
1101001100 => 1110001100 => 2
1101010010 => 1110100100 => 3
1101010100 => 1111000010 => 2
1101011000 => 1011011000 => 3
1101100010 => 1001111000 => 2
1101100100 => 1101010100 => 4
1101101000 => 1011001100 => 3
1101110000 => 1000111100 => 2
1110010010 => 1100110010 => 3
1110010100 => 1110010010 => 3
1110100010 => 1010101010 => 5
1110110000 => 1001011010 => 4
1111000010 => 1000110110 => 3
1111000100 => 1010010110 => 4
1111010000 => 1001001110 => 3
1111100000 => 1000011110 => 2
101010101010 => 111111000000 => 1
101010101100 => 101111100000 => 2
101010110010 => 101111100000 => 2
101010110100 => 110111010000 => 3
101011001010 => 101111100000 => 2
101011001100 => 110101110000 => 3
101011010010 => 110111010000 => 3
101011010100 => 111011001000 => 3
101011011000 => 100111101000 => 3
101011100100 => 110011100010 => 3
101011101000 => 101011010010 => 5
101100101010 => 101111100000 => 2
101100101100 => 110011110000 => 2
101100110010 => 110101110000 => 3
101100110100 => 111010011000 => 3
101100111000 => 101010110100 => 5
101101001010 => 110111010000 => 3
101101001100 => 111001101000 => 3
101101010010 => 111011001000 => 3
101101010100 => 111101000100 => 3
101101011000 => 101011110000 => 3
101101100010 => 100111101000 => 3
101101100100 => 110011101000 => 3
101101101000 => 101011011000 => 4
101101110000 => 100011101100 => 3
101110010010 => 110011100010 => 3
101110010100 => 111001100010 => 3
101110100010 => 101011010010 => 5
101110100100 => 111001001010 => 4
101110101000 => 101101001010 => 5
110010101010 => 101111100000 => 2
110010101100 => 110101110000 => 3
110010110010 => 110011110000 => 2
110010110100 => 111001101000 => 3
110011001010 => 110101110000 => 3
110011001100 => 111000111000 => 2
110011010010 => 111010011000 => 3
110011010100 => 111100010100 => 3
110011011000 => 101100111000 => 3
110011100010 => 101010110100 => 5
110011100100 => 111000101100 => 3
110100101010 => 110111010000 => 3
110100101100 => 111010011000 => 3
110100110010 => 111001101000 => 3
110100110100 => 111100001100 => 2
110100111000 => 101100101100 => 4
110101001010 => 111011001000 => 3
110101001100 => 111100010100 => 3
110101010010 => 111101000100 => 3
110101010100 => 111110000010 => 2
110101011000 => 101110110000 => 3
110101100010 => 101011110000 => 3
110101100100 => 110110101000 => 4
110101101000 => 101110011000 => 3
110101110000 => 100101110100 => 4
110110001010 => 100111101000 => 3
110110001100 => 101100111000 => 3
110110010010 => 110011101000 => 3
110110010100 => 111010100100 => 4
110110011000 => 110010111000 => 3
110110100010 => 101011011000 => 4
110110100100 => 111010001100 => 3
110110101000 => 101110001100 => 3
110111000010 => 100011101100 => 3
111000101100 => 101010110100 => 5
111000110100 => 101100101100 => 4
111001001010 => 110011100010 => 3
111001001100 => 111000101100 => 3
111001010010 => 111001100010 => 3
111001010100 => 111100100010 => 3
111001011000 => 110010110010 => 4
111001100100 => 111000110010 => 3
111010001010 => 101011010010 => 5
111010010010 => 111001001010 => 4
111010010100 => 111100001010 => 3
111010011000 => 110100101010 => 5
111010100010 => 101101001010 => 5
111011000100 => 101010101010 => 6
1111111110 => 1111111110 => 1
1111111001 => 1011111110 => 2
1111101011 => 1110111110 => 2
1111100111 => 1011111110 => 2
1111100001 => 1000111110 => 2
1110011111 => 1011111110 => 2
1110000111 => 1000111110 => 2
1110000001 => 1000001110 => 2
1101011111 => 1110111110 => 2
1101000011 => 1001001110 => 3
1100001011 => 1000110110 => 3
1011111110 => 1110111110 => 2
1001111111 => 1011111110 => 2
1000101110 => 1010101010 => 5
1000011111 => 1000111110 => 2
1000011110 => 1001001110 => 3
1000000111 => 1000001110 => 2
1000000001 => 1000000010 => 2
1000000000 => 1000000000 => 1
10000000000 => 10000000000 => 1
11111111110 => 11111111110 => 1
0111111111 => 1111111110 => 1
0111111101 => 1110111110 => 2
0111100001 => 1000110110 => 3
0000000001 => 1000000000 => 1
01111111111 => 11111111110 => 1
0111010001 => 1010101010 => 5
00000000001 => 10000000000 => 1
0101010101 => 1111100000 => 1
0101010011 => 1111000010 => 2
0101001101 => 1111000010 => 2
0101001011 => 1110100100 => 3
0100110101 => 1111000010 => 2
0100110011 => 1110001100 => 2
0100101101 => 1110100100 => 3
0100101011 => 1101101000 => 3
0100011011 => 1011001100 => 3
0100010111 => 1010101010 => 5
0100001111 => 1001001110 => 3
0011010101 => 1111000010 => 2
0011010011 => 1110001100 => 2
0011001101 => 1110001100 => 2
0011001011 => 1100111000 => 2
0010110101 => 1110100100 => 3
0010110011 => 1100111000 => 2
0010101101 => 1101101000 => 3
0010101011 => 1011110000 => 2
0010100111 => 1110010010 => 3
0010011011 => 1101010100 => 4
0010010111 => 1100110010 => 3
0001101101 => 1011001100 => 3
0001101011 => 1011011000 => 3
0001011101 => 1010101010 => 5
0001011011 => 1001111000 => 2
0001001111 => 1010010110 => 4
0000111101 => 1001001110 => 3
0000111011 => 1001011010 => 4
0000110111 => 1000111100 => 2
0000101111 => 1000110110 => 3
0000011111 => 1000011110 => 2
010101010101 => 111111000000 => 1
010101010011 => 111110000010 => 2
010101001101 => 111110000010 => 2
010101001011 => 111101000100 => 3
010100110101 => 111110000010 => 2
010100110011 => 111100010100 => 3
010100101101 => 111101000100 => 3
010100101011 => 111011001000 => 3
010100011011 => 101110001100 => 3
010100010111 => 101101001010 => 5
010011010101 => 111110000010 => 2
010011010011 => 111100001100 => 2
010011001101 => 111100010100 => 3
010011001011 => 111001101000 => 3
010011000111 => 110100101010 => 5
010010110101 => 111101000100 => 3
010010110011 => 111010011000 => 3
010010101101 => 111011001000 => 3
010010101011 => 110111010000 => 3
010010100111 => 111100001010 => 3
010010011011 => 111010001100 => 3
010010010111 => 111001001010 => 4
010001101101 => 101110001100 => 3
010001101011 => 101110011000 => 3
010001011101 => 101101001010 => 5
010001011011 => 101011011000 => 4
010001010111 => 101011010010 => 5
001101010101 => 111110000010 => 2
001101010011 => 111100010100 => 3
001101001101 => 111100001100 => 2
001101001011 => 111010011000 => 3
001100110101 => 111100010100 => 3
001100110011 => 111000111000 => 2
001100101101 => 111001101000 => 3
001100101011 => 110101110000 => 3
001100100111 => 111000110010 => 3
001100011101 => 110100101010 => 5
001100011011 => 110010111000 => 3
001011010101 => 111101000100 => 3
001011010011 => 111001101000 => 3
001011001101 => 111010011000 => 3
001011001011 => 110011110000 => 2
001011000111 => 110010110010 => 4
001010110101 => 111011001000 => 3
001010110011 => 110101110000 => 3
001010101101 => 110111010000 => 3
001010101011 => 101111100000 => 2
001010100111 => 111100100010 => 3
001010011101 => 111100001010 => 3
001010011011 => 111010100100 => 4
001010010111 => 111001100010 => 3
001001110011 => 111000110010 => 3
001001101101 => 111010001100 => 3
001001101011 => 110110101000 => 4
001001100111 => 111000101100 => 3
001001011101 => 111001001010 => 4
001001011011 => 110011101000 => 3
001001010111 => 110011100010 => 3
000111010011 => 110100101010 => 5
000111001011 => 110010110010 => 4
000110110101 => 101110001100 => 3
000110110011 => 110010111000 => 3
000110101101 => 101110011000 => 3
000110101011 => 101110110000 => 3
000110100111 => 101100101100 => 4
000110011011 => 101100111000 => 3
000101110101 => 101101001010 => 5
000101101101 => 101011011000 => 4
000101101011 => 101011110000 => 3
000101100111 => 101010110100 => 5
000101011101 => 101011010010 => 5
000101011011 => 100111101000 => 3
000100111011 => 101010101010 => 6
000011010111 => 100101110100 => 4
000010110111 => 100011101100 => 3
100110011001 => 111000111000 => 2
100110001101 => 110010111000 => 3
100110110001 => 101100111000 => 3
100110100101 => 111010011000 => 3
100011011001 => 110010111000 => 3
100011001101 => 101100111000 => 3
100011100101 => 110010110010 => 4
100010011101 => 101010101010 => 6
100010110101 => 101011110000 => 3
101100011001 => 101100111000 => 3
101100110001 => 110010111000 => 3
101100100101 => 110011101000 => 3
101110000101 => 100011101100 => 3
101001011001 => 111010011000 => 3
101001001101 => 111010001100 => 3
101001110001 => 101100101100 => 4
101001100101 => 111001101000 => 3
101000110101 => 101110011000 => 3
101011010001 => 101110011000 => 3
101011000101 => 101011110000 => 3
101010010101 => 111011001000 => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 2,6 2,10,4 2,20,10 2,20,42 2,42,70,14 2,42,140,72 2,60,288,126,36
$F_{1} = 2$
$F_{2} = 2 + 2\ q$
$F_{3} = 2 + 6\ q$
$F_{4} = 2 + 10\ q + 4\ q^{2}$
$F_{5} = 2 + 20\ q + 10\ q^{2}$
$F_{6} = 2 + 20\ q + 42\ q^{2}$
$F_{7} = 2 + 42\ q + 70\ q^{2} + 14\ q^{3}$
$F_{8} = 2 + 42\ q + 140\ q^{2} + 72\ q^{3}$
$F_{9} = 2 + 60\ q + 288\ q^{2} + 126\ q^{3} + 36\ q^{4}$
Description
The number of descents of a binary word.
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Burrows-Wheeler
Description
The Burrows-Wheeler transform of a binary word.
The Burrows-Wheeler transform of a finite word $w$ is obtained from $w$ by first listing the conjugates of $w$ in lexicographic order and then concatenating the final letters of the conjugates in this order.
The Burrows-Wheeler transform of a finite word $w$ is obtained from $w$ by first listing the conjugates of $w$ in lexicographic order and then concatenating the final letters of the conjugates in this order.
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