Identifier
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Images
0 => 0 => 0
1 => 1 => 1
00 => 00 => 00
01 => 10 => 10
10 => 01 => 01
11 => 11 => 11
000 => 000 => 000
001 => 010 => 100
010 => 100 => 010
011 => 110 => 110
100 => 001 => 001
101 => 011 => 011
110 => 101 => 101
111 => 111 => 111
0000 => 0000 => 0000
0001 => 0010 => 1000
0010 => 0100 => 0100
0011 => 0110 => 1100
0100 => 1000 => 0010
0101 => 1010 => 0110
0110 => 1100 => 1010
0111 => 1110 => 1110
1000 => 0001 => 0001
1001 => 0011 => 0011
1010 => 0101 => 1001
1011 => 0111 => 0111
1100 => 1001 => 0101
1101 => 1011 => 1011
1110 => 1101 => 1101
1111 => 1111 => 1111
00000 => 00000 => 00000
00001 => 00010 => 10000
00010 => 00100 => 01000
00011 => 00110 => 11000
00100 => 01000 => 00100
00101 => 01010 => 01100
00110 => 01100 => 10100
00111 => 01110 => 11100
01000 => 10000 => 00010
01001 => 10010 => 00110
01010 => 10100 => 10010
01011 => 10110 => 01110
01100 => 11000 => 01010
01101 => 11010 => 10110
01110 => 11100 => 11010
01111 => 11110 => 11110
10000 => 00001 => 00001
10001 => 00011 => 00011
10010 => 00101 => 10001
10011 => 00111 => 00111
10100 => 01001 => 01001
10101 => 01011 => 10011
10110 => 01101 => 11001
10111 => 01111 => 01111
11000 => 10001 => 00101
11001 => 10011 => 01011
11010 => 10101 => 01101
11011 => 10111 => 10111
11100 => 11001 => 10101
11101 => 11011 => 11011
11110 => 11101 => 11101
11111 => 11111 => 11111
000000 => 000000 => 000000
000001 => 000010 => 100000
000010 => 000100 => 010000
000011 => 000110 => 110000
000100 => 001000 => 001000
000101 => 001010 => 011000
000110 => 001100 => 101000
000111 => 001110 => 111000
001000 => 010000 => 000100
001001 => 010010 => 001100
001010 => 010100 => 100100
001011 => 010110 => 011100
001100 => 011000 => 010100
001101 => 011010 => 101100
001110 => 011100 => 110100
001111 => 011110 => 111100
010000 => 100000 => 000010
010001 => 100010 => 000110
010010 => 100100 => 100010
010011 => 100110 => 001110
010100 => 101000 => 010010
010101 => 101010 => 100110
010110 => 101100 => 110010
010111 => 101110 => 011110
011000 => 110000 => 001010
011001 => 110010 => 010110
011010 => 110100 => 011010
011011 => 110110 => 101110
011100 => 111000 => 101010
011101 => 111010 => 110110
011110 => 111100 => 111010
011111 => 111110 => 111110
100000 => 000001 => 000001
100001 => 000011 => 000011
100010 => 000101 => 100001
100011 => 000111 => 000111
100100 => 001001 => 010001
100101 => 001011 => 100011
100110 => 001101 => 110001
>>> Load all 1049 entries. <<<
100111 => 001111 => 001111
101000 => 010001 => 001001
101001 => 010011 => 010011
101010 => 010101 => 011001
101011 => 010111 => 100111
101100 => 011001 => 101001
101101 => 011011 => 110011
101110 => 011101 => 111001
101111 => 011111 => 011111
110000 => 100001 => 000101
110001 => 100011 => 001011
110010 => 100101 => 001101
110011 => 100111 => 010111
110100 => 101001 => 100101
110101 => 101011 => 011011
110110 => 101101 => 011101
110111 => 101111 => 101111
111000 => 110001 => 010101
111001 => 110011 => 101011
111010 => 110101 => 101101
111011 => 110111 => 110111
111100 => 111001 => 110101
111101 => 111011 => 111011
111110 => 111101 => 111101
111111 => 111111 => 111111
0000000 => 0000000 => 0000000
0000001 => 0000010 => 1000000
0000010 => 0000100 => 0100000
0000011 => 0000110 => 1100000
0000100 => 0001000 => 0010000
0000101 => 0001010 => 0110000
0000110 => 0001100 => 1010000
0000111 => 0001110 => 1110000
0001000 => 0010000 => 0001000
0001001 => 0010010 => 0011000
0001010 => 0010100 => 1001000
0001011 => 0010110 => 0111000
0001100 => 0011000 => 0101000
0001101 => 0011010 => 1011000
0001110 => 0011100 => 1101000
0001111 => 0011110 => 1111000
0010000 => 0100000 => 0000100
0010001 => 0100010 => 0001100
0010010 => 0100100 => 1000100
0010011 => 0100110 => 0011100
0010100 => 0101000 => 0100100
0010101 => 0101010 => 1001100
0010110 => 0101100 => 1100100
0010111 => 0101110 => 0111100
0011000 => 0110000 => 0010100
0011001 => 0110010 => 0101100
0011010 => 0110100 => 0110100
0011011 => 0110110 => 1011100
0011100 => 0111000 => 1010100
0011101 => 0111010 => 1101100
0011110 => 0111100 => 1110100
0011111 => 0111110 => 1111100
0100000 => 1000000 => 0000010
0100001 => 1000010 => 0000110
0100010 => 1000100 => 1000010
0100011 => 1000110 => 0001110
0100100 => 1001000 => 0100010
0100101 => 1001010 => 1000110
0100110 => 1001100 => 1100010
0100111 => 1001110 => 0011110
0101000 => 1010000 => 0010010
0101001 => 1010010 => 0100110
0101010 => 1010100 => 0110010
0101011 => 1010110 => 1001110
0101100 => 1011000 => 1010010
0101101 => 1011010 => 1100110
0101110 => 1011100 => 1110010
0101111 => 1011110 => 0111110
0110000 => 1100000 => 0001010
0110001 => 1100010 => 0010110
0110010 => 1100100 => 0011010
0110011 => 1100110 => 0101110
0110100 => 1101000 => 1001010
0110101 => 1101010 => 0110110
0110110 => 1101100 => 0111010
0110111 => 1101110 => 1011110
0111000 => 1110000 => 0101010
0111001 => 1110010 => 1010110
0111010 => 1110100 => 1011010
0111011 => 1110110 => 1101110
0111100 => 1111000 => 1101010
0111101 => 1111010 => 1110110
0111110 => 1111100 => 1111010
0111111 => 1111110 => 1111110
1000000 => 0000001 => 0000001
1000001 => 0000011 => 0000011
1000010 => 0000101 => 1000001
1000011 => 0000111 => 0000111
1000100 => 0001001 => 0100001
1000101 => 0001011 => 1000011
1000110 => 0001101 => 1100001
1000111 => 0001111 => 0001111
1001000 => 0010001 => 0010001
1001001 => 0010011 => 0100011
1001010 => 0010101 => 0110001
1001011 => 0010111 => 1000111
1001100 => 0011001 => 1010001
1001101 => 0011011 => 1100011
1001110 => 0011101 => 1110001
1001111 => 0011111 => 0011111
1010000 => 0100001 => 0001001
1010001 => 0100011 => 0010011
1010010 => 0100101 => 0011001
1010011 => 0100111 => 0100111
1010100 => 0101001 => 1001001
1010101 => 0101011 => 0110011
1010110 => 0101101 => 0111001
1010111 => 0101111 => 1001111
1011000 => 0110001 => 0101001
1011001 => 0110011 => 1010011
1011010 => 0110101 => 1011001
1011011 => 0110111 => 1100111
1011100 => 0111001 => 1101001
1011101 => 0111011 => 1110011
1011110 => 0111101 => 1111001
1011111 => 0111111 => 0111111
1100000 => 1000001 => 0000101
1100001 => 1000011 => 0001011
1100010 => 1000101 => 0001101
1100011 => 1000111 => 0010111
1100100 => 1001001 => 1000101
1100101 => 1001011 => 0011011
1100110 => 1001101 => 0011101
1100111 => 1001111 => 0101111
1101000 => 1010001 => 0100101
1101001 => 1010011 => 1001011
1101010 => 1010101 => 1001101
1101011 => 1010111 => 0110111
1101100 => 1011001 => 1100101
1101101 => 1011011 => 0111011
1101110 => 1011101 => 0111101
1101111 => 1011111 => 1011111
1110000 => 1100001 => 0010101
1110001 => 1100011 => 0101011
1110010 => 1100101 => 0101101
1110011 => 1100111 => 1010111
1110100 => 1101001 => 0110101
1110101 => 1101011 => 1011011
1110110 => 1101101 => 1011101
1110111 => 1101111 => 1101111
1111000 => 1110001 => 1010101
1111001 => 1110011 => 1101011
1111010 => 1110101 => 1101101
1111011 => 1110111 => 1110111
1111100 => 1111001 => 1110101
1111101 => 1111011 => 1111011
1111110 => 1111101 => 1111101
1111111 => 1111111 => 1111111
00000000 => 00000000 => 00000000
00000001 => 00000010 => 10000000
00000010 => 00000100 => 01000000
00000011 => 00000110 => 11000000
00000100 => 00001000 => 00100000
00000101 => 00001010 => 01100000
00000110 => 00001100 => 10100000
00000111 => 00001110 => 11100000
00001000 => 00010000 => 00010000
00001001 => 00010010 => 00110000
00001010 => 00010100 => 10010000
00001011 => 00010110 => 01110000
00001100 => 00011000 => 01010000
00001101 => 00011010 => 10110000
00001110 => 00011100 => 11010000
00001111 => 00011110 => 11110000
00010000 => 00100000 => 00001000
00010001 => 00100010 => 00011000
00010010 => 00100100 => 10001000
00010011 => 00100110 => 00111000
00010100 => 00101000 => 01001000
00010101 => 00101010 => 10011000
00010110 => 00101100 => 11001000
00010111 => 00101110 => 01111000
00011000 => 00110000 => 00101000
00011001 => 00110010 => 01011000
00011010 => 00110100 => 01101000
00011011 => 00110110 => 10111000
00011100 => 00111000 => 10101000
00011101 => 00111010 => 11011000
00011110 => 00111100 => 11101000
00011111 => 00111110 => 11111000
00100000 => 01000000 => 00000100
00100001 => 01000010 => 00001100
00100010 => 01000100 => 10000100
00100011 => 01000110 => 00011100
00100100 => 01001000 => 01000100
00100101 => 01001010 => 10001100
00100110 => 01001100 => 11000100
00100111 => 01001110 => 00111100
00101000 => 01010000 => 00100100
00101001 => 01010010 => 01001100
00101010 => 01010100 => 01100100
00101011 => 01010110 => 10011100
00101100 => 01011000 => 10100100
00101101 => 01011010 => 11001100
00101110 => 01011100 => 11100100
00101111 => 01011110 => 01111100
00110000 => 01100000 => 00010100
00110001 => 01100010 => 00101100
00110010 => 01100100 => 00110100
00110011 => 01100110 => 01011100
00110100 => 01101000 => 10010100
00110101 => 01101010 => 01101100
00110110 => 01101100 => 01110100
00110111 => 01101110 => 10111100
00111000 => 01110000 => 01010100
00111001 => 01110010 => 10101100
00111010 => 01110100 => 10110100
00111011 => 01110110 => 11011100
00111100 => 01111000 => 11010100
00111101 => 01111010 => 11101100
00111110 => 01111100 => 11110100
00111111 => 01111110 => 11111100
01000000 => 10000000 => 00000010
01000001 => 10000010 => 00000110
01000010 => 10000100 => 10000010
01000011 => 10000110 => 00001110
01000100 => 10001000 => 01000010
01000101 => 10001010 => 10000110
01000110 => 10001100 => 11000010
01000111 => 10001110 => 00011110
01001000 => 10010000 => 00100010
01001001 => 10010010 => 01000110
01001010 => 10010100 => 01100010
01001011 => 10010110 => 10001110
01001100 => 10011000 => 10100010
01001101 => 10011010 => 11000110
01001110 => 10011100 => 11100010
01001111 => 10011110 => 00111110
01010000 => 10100000 => 00010010
01010001 => 10100010 => 00100110
01010010 => 10100100 => 00110010
01010011 => 10100110 => 01001110
01010100 => 10101000 => 10010010
01010101 => 10101010 => 01100110
01010110 => 10101100 => 01110010
01010111 => 10101110 => 10011110
01011000 => 10110000 => 01010010
01011001 => 10110010 => 10100110
01011010 => 10110100 => 10110010
01011011 => 10110110 => 11001110
01011100 => 10111000 => 11010010
01011101 => 10111010 => 11100110
01011110 => 10111100 => 11110010
01011111 => 10111110 => 01111110
01100000 => 11000000 => 00001010
01100001 => 11000010 => 00010110
01100010 => 11000100 => 00011010
01100011 => 11000110 => 00101110
01100100 => 11001000 => 10001010
01100101 => 11001010 => 00110110
01100110 => 11001100 => 00111010
01100111 => 11001110 => 01011110
01101000 => 11010000 => 01001010
01101001 => 11010010 => 10010110
01101010 => 11010100 => 10011010
01101011 => 11010110 => 01101110
01101100 => 11011000 => 11001010
01101101 => 11011010 => 01110110
01101110 => 11011100 => 01111010
01101111 => 11011110 => 10111110
01110000 => 11100000 => 00101010
01110001 => 11100010 => 01010110
01110010 => 11100100 => 01011010
01110011 => 11100110 => 10101110
01110100 => 11101000 => 01101010
01110101 => 11101010 => 10110110
01110110 => 11101100 => 10111010
01110111 => 11101110 => 11011110
01111000 => 11110000 => 10101010
01111001 => 11110010 => 11010110
01111010 => 11110100 => 11011010
01111011 => 11110110 => 11101110
01111100 => 11111000 => 11101010
01111101 => 11111010 => 11110110
01111110 => 11111100 => 11111010
01111111 => 11111110 => 11111110
10000000 => 00000001 => 00000001
10000001 => 00000011 => 00000011
10000010 => 00000101 => 10000001
10000011 => 00000111 => 00000111
10000100 => 00001001 => 01000001
10000101 => 00001011 => 10000011
10000110 => 00001101 => 11000001
10000111 => 00001111 => 00001111
10001000 => 00010001 => 00100001
10001001 => 00010011 => 01000011
10001010 => 00010101 => 01100001
10001011 => 00010111 => 10000111
10001100 => 00011001 => 10100001
10001101 => 00011011 => 11000011
10001110 => 00011101 => 11100001
10001111 => 00011111 => 00011111
10010000 => 00100001 => 00010001
10010001 => 00100011 => 00100011
10010010 => 00100101 => 00110001
10010011 => 00100111 => 01000111
10010100 => 00101001 => 10010001
10010101 => 00101011 => 01100011
10010110 => 00101101 => 01110001
10010111 => 00101111 => 10001111
10011000 => 00110001 => 01010001
10011001 => 00110011 => 10100011
10011010 => 00110101 => 10110001
10011011 => 00110111 => 11000111
10011100 => 00111001 => 11010001
10011101 => 00111011 => 11100011
10011110 => 00111101 => 11110001
10011111 => 00111111 => 00111111
10100000 => 01000001 => 00001001
10100001 => 01000011 => 00010011
10100010 => 01000101 => 00011001
10100011 => 01000111 => 00100111
10100100 => 01001001 => 10001001
10100101 => 01001011 => 00110011
10100110 => 01001101 => 00111001
10100111 => 01001111 => 01001111
10101000 => 01010001 => 01001001
10101001 => 01010011 => 10010011
10101010 => 01010101 => 10011001
10101011 => 01010111 => 01100111
10101100 => 01011001 => 11001001
10101101 => 01011011 => 01110011
10101110 => 01011101 => 01111001
10101111 => 01011111 => 10011111
10110000 => 01100001 => 00101001
10110001 => 01100011 => 01010011
10110010 => 01100101 => 01011001
10110011 => 01100111 => 10100111
10110100 => 01101001 => 01101001
10110101 => 01101011 => 10110011
10110110 => 01101101 => 10111001
10110111 => 01101111 => 11001111
10111000 => 01110001 => 10101001
10111001 => 01110011 => 11010011
10111010 => 01110101 => 11011001
10111011 => 01110111 => 11100111
10111100 => 01111001 => 11101001
10111101 => 01111011 => 11110011
10111110 => 01111101 => 11111001
10111111 => 01111111 => 01111111
11000000 => 10000001 => 00000101
11000001 => 10000011 => 00001011
11000010 => 10000101 => 00001101
11000011 => 10000111 => 00010111
11000100 => 10001001 => 10000101
11000101 => 10001011 => 00011011
11000110 => 10001101 => 00011101
11000111 => 10001111 => 00101111
11001000 => 10010001 => 01000101
11001001 => 10010011 => 10001011
11001010 => 10010101 => 10001101
11001011 => 10010111 => 00110111
11001100 => 10011001 => 11000101
11001101 => 10011011 => 00111011
11001110 => 10011101 => 00111101
11001111 => 10011111 => 01011111
11010000 => 10100001 => 00100101
11010001 => 10100011 => 01001011
11010010 => 10100101 => 01001101
11010011 => 10100111 => 10010111
11010100 => 10101001 => 01100101
11010101 => 10101011 => 10011011
11010110 => 10101101 => 10011101
11010111 => 10101111 => 01101111
11011000 => 10110001 => 10100101
11011001 => 10110011 => 11001011
11011010 => 10110101 => 11001101
11011011 => 10110111 => 01110111
11011100 => 10111001 => 11100101
11011101 => 10111011 => 01111011
11011110 => 10111101 => 01111101
11011111 => 10111111 => 10111111
11100000 => 11000001 => 00010101
11100001 => 11000011 => 00101011
11100010 => 11000101 => 00101101
11100011 => 11000111 => 01010111
11100100 => 11001001 => 00110101
11100101 => 11001011 => 01011011
11100110 => 11001101 => 01011101
11100111 => 11001111 => 10101111
11101000 => 11010001 => 10010101
11101001 => 11010011 => 01101011
11101010 => 11010101 => 01101101
11101011 => 11010111 => 10110111
11101100 => 11011001 => 01110101
11101101 => 11011011 => 10111011
11101110 => 11011101 => 10111101
11101111 => 11011111 => 11011111
11110000 => 11100001 => 01010101
11110001 => 11100011 => 10101011
11110010 => 11100101 => 10101101
11110011 => 11100111 => 11010111
11110100 => 11101001 => 10110101
11110101 => 11101011 => 11011011
11110110 => 11101101 => 11011101
11110111 => 11101111 => 11101111
11111000 => 11110001 => 11010101
11111001 => 11110011 => 11101011
11111010 => 11110101 => 11101101
11111011 => 11110111 => 11110111
11111100 => 11111001 => 11110101
11111101 => 11111011 => 11111011
11111110 => 11111101 => 11111101
11111111 => 11111111 => 11111111
000000000 => 000000000 => 000000000
000000001 => 000000010 => 100000000
000000010 => 000000100 => 010000000
000000011 => 000000110 => 110000000
000000100 => 000001000 => 001000000
000000101 => 000001010 => 011000000
000000110 => 000001100 => 101000000
000000111 => 000001110 => 111000000
000001000 => 000010000 => 000100000
000001001 => 000010010 => 001100000
000001010 => 000010100 => 100100000
000001011 => 000010110 => 011100000
000001100 => 000011000 => 010100000
000001101 => 000011010 => 101100000
000001110 => 000011100 => 110100000
000001111 => 000011110 => 111100000
000010000 => 000100000 => 000010000
000010001 => 000100010 => 000110000
000010010 => 000100100 => 100010000
000010011 => 000100110 => 001110000
000010100 => 000101000 => 010010000
000010101 => 000101010 => 100110000
000010110 => 000101100 => 110010000
000010111 => 000101110 => 011110000
000011000 => 000110000 => 001010000
000011001 => 000110010 => 010110000
000011010 => 000110100 => 011010000
000011011 => 000110110 => 101110000
000011100 => 000111000 => 101010000
000011101 => 000111010 => 110110000
000011110 => 000111100 => 111010000
000011111 => 000111110 => 111110000
000100000 => 001000000 => 000001000
000100001 => 001000010 => 000011000
000100010 => 001000100 => 100001000
000100011 => 001000110 => 000111000
000100100 => 001001000 => 010001000
000100101 => 001001010 => 100011000
000100110 => 001001100 => 110001000
000100111 => 001001110 => 001111000
000101000 => 001010000 => 001001000
000101001 => 001010010 => 010011000
000101010 => 001010100 => 011001000
000101011 => 001010110 => 100111000
000101100 => 001011000 => 101001000
000101101 => 001011010 => 110011000
000101110 => 001011100 => 111001000
000101111 => 001011110 => 011111000
000110000 => 001100000 => 000101000
000110001 => 001100010 => 001011000
000110010 => 001100100 => 001101000
000110011 => 001100110 => 010111000
000110100 => 001101000 => 100101000
000110101 => 001101010 => 011011000
000110110 => 001101100 => 011101000
000110111 => 001101110 => 101111000
000111000 => 001110000 => 010101000
000111001 => 001110010 => 101011000
000111010 => 001110100 => 101101000
000111011 => 001110110 => 110111000
000111100 => 001111000 => 110101000
000111101 => 001111010 => 111011000
000111110 => 001111100 => 111101000
000111111 => 001111110 => 111111000
001000000 => 010000000 => 000000100
001000001 => 010000010 => 000001100
001000010 => 010000100 => 100000100
001000011 => 010000110 => 000011100
001000100 => 010001000 => 010000100
001000101 => 010001010 => 100001100
001000110 => 010001100 => 110000100
001000111 => 010001110 => 000111100
001001000 => 010010000 => 001000100
001001001 => 010010010 => 010001100
001001010 => 010010100 => 011000100
001001011 => 010010110 => 100011100
001001100 => 010011000 => 101000100
001001101 => 010011010 => 110001100
001001110 => 010011100 => 111000100
001001111 => 010011110 => 001111100
001010000 => 010100000 => 000100100
001010001 => 010100010 => 001001100
001010010 => 010100100 => 001100100
001010011 => 010100110 => 010011100
001010100 => 010101000 => 100100100
001010101 => 010101010 => 011001100
001010110 => 010101100 => 011100100
001010111 => 010101110 => 100111100
001011000 => 010110000 => 010100100
001011001 => 010110010 => 101001100
001011010 => 010110100 => 101100100
001011011 => 010110110 => 110011100
001011100 => 010111000 => 110100100
001011101 => 010111010 => 111001100
001011110 => 010111100 => 111100100
001011111 => 010111110 => 011111100
001100000 => 011000000 => 000010100
001100001 => 011000010 => 000101100
001100010 => 011000100 => 000110100
001100011 => 011000110 => 001011100
001100100 => 011001000 => 100010100
001100101 => 011001010 => 001101100
001100110 => 011001100 => 001110100
001100111 => 011001110 => 010111100
001101000 => 011010000 => 010010100
001101001 => 011010010 => 100101100
001101010 => 011010100 => 100110100
001101011 => 011010110 => 011011100
001101100 => 011011000 => 110010100
001101101 => 011011010 => 011101100
001101110 => 011011100 => 011110100
001101111 => 011011110 => 101111100
001110000 => 011100000 => 001010100
001110001 => 011100010 => 010101100
001110010 => 011100100 => 010110100
001110011 => 011100110 => 101011100
001110100 => 011101000 => 011010100
001110101 => 011101010 => 101101100
001110110 => 011101100 => 101110100
001110111 => 011101110 => 110111100
001111000 => 011110000 => 101010100
001111001 => 011110010 => 110101100
001111010 => 011110100 => 110110100
001111011 => 011110110 => 111011100
001111100 => 011111000 => 111010100
001111101 => 011111010 => 111101100
001111110 => 011111100 => 111110100
001111111 => 011111110 => 111111100
010000000 => 100000000 => 000000010
010000001 => 100000010 => 000000110
010000010 => 100000100 => 100000010
010000011 => 100000110 => 000001110
010000100 => 100001000 => 010000010
010000101 => 100001010 => 100000110
010000110 => 100001100 => 110000010
010000111 => 100001110 => 000011110
010001000 => 100010000 => 001000010
010001001 => 100010010 => 010000110
010001010 => 100010100 => 011000010
010001011 => 100010110 => 100001110
010001100 => 100011000 => 101000010
010001101 => 100011010 => 110000110
010001110 => 100011100 => 111000010
010001111 => 100011110 => 000111110
010010000 => 100100000 => 000100010
010010001 => 100100010 => 001000110
010010010 => 100100100 => 001100010
010010011 => 100100110 => 010001110
010010100 => 100101000 => 100100010
010010101 => 100101010 => 011000110
010010110 => 100101100 => 011100010
010010111 => 100101110 => 100011110
010011000 => 100110000 => 010100010
010011001 => 100110010 => 101000110
010011010 => 100110100 => 101100010
010011011 => 100110110 => 110001110
010011100 => 100111000 => 110100010
010011101 => 100111010 => 111000110
010011110 => 100111100 => 111100010
010011111 => 100111110 => 001111110
010100000 => 101000000 => 000010010
010100001 => 101000010 => 000100110
010100010 => 101000100 => 000110010
010100011 => 101000110 => 001001110
010100100 => 101001000 => 100010010
010100101 => 101001010 => 001100110
010100110 => 101001100 => 001110010
010100111 => 101001110 => 010011110
010101000 => 101010000 => 010010010
010101001 => 101010010 => 100100110
010101010 => 101010100 => 100110010
010101011 => 101010110 => 011001110
010101100 => 101011000 => 110010010
010101101 => 101011010 => 011100110
010101110 => 101011100 => 011110010
010101111 => 101011110 => 100111110
010110000 => 101100000 => 001010010
010110001 => 101100010 => 010100110
010110010 => 101100100 => 010110010
010110011 => 101100110 => 101001110
010110100 => 101101000 => 011010010
010110101 => 101101010 => 101100110
010110110 => 101101100 => 101110010
010110111 => 101101110 => 110011110
010111000 => 101110000 => 101010010
010111001 => 101110010 => 110100110
010111010 => 101110100 => 110110010
010111011 => 101110110 => 111001110
010111100 => 101111000 => 111010010
010111101 => 101111010 => 111100110
010111110 => 101111100 => 111110010
010111111 => 101111110 => 011111110
011000000 => 110000000 => 000001010
011000001 => 110000010 => 000010110
011000010 => 110000100 => 000011010
011000011 => 110000110 => 000101110
011000100 => 110001000 => 100001010
011000101 => 110001010 => 000110110
011000110 => 110001100 => 000111010
011000111 => 110001110 => 001011110
011001000 => 110010000 => 010001010
011001001 => 110010010 => 100010110
011001010 => 110010100 => 100011010
011001011 => 110010110 => 001101110
011001100 => 110011000 => 110001010
011001101 => 110011010 => 001110110
011001110 => 110011100 => 001111010
011001111 => 110011110 => 010111110
011010000 => 110100000 => 001001010
011010001 => 110100010 => 010010110
011010010 => 110100100 => 010011010
011010011 => 110100110 => 100101110
011010100 => 110101000 => 011001010
011010101 => 110101010 => 100110110
011010110 => 110101100 => 100111010
011010111 => 110101110 => 011011110
011011000 => 110110000 => 101001010
011011001 => 110110010 => 110010110
011011010 => 110110100 => 110011010
011011011 => 110110110 => 011101110
011011100 => 110111000 => 111001010
011011101 => 110111010 => 011110110
011011110 => 110111100 => 011111010
011011111 => 110111110 => 101111110
011100000 => 111000000 => 000101010
011100001 => 111000010 => 001010110
011100010 => 111000100 => 001011010
011100011 => 111000110 => 010101110
011100100 => 111001000 => 001101010
011100101 => 111001010 => 010110110
011100110 => 111001100 => 010111010
011100111 => 111001110 => 101011110
011101000 => 111010000 => 100101010
011101001 => 111010010 => 011010110
011101010 => 111010100 => 011011010
011101011 => 111010110 => 101101110
011101100 => 111011000 => 011101010
011101101 => 111011010 => 101110110
011101110 => 111011100 => 101111010
011101111 => 111011110 => 110111110
011110000 => 111100000 => 010101010
011110001 => 111100010 => 101010110
011110010 => 111100100 => 101011010
011110011 => 111100110 => 110101110
011110100 => 111101000 => 101101010
011110101 => 111101010 => 110110110
011110110 => 111101100 => 110111010
011110111 => 111101110 => 111011110
011111000 => 111110000 => 110101010
011111001 => 111110010 => 111010110
011111010 => 111110100 => 111011010
011111011 => 111110110 => 111101110
011111100 => 111111000 => 111101010
011111101 => 111111010 => 111110110
011111110 => 111111100 => 111111010
011111111 => 111111110 => 111111110
100000000 => 000000001 => 000000001
100000001 => 000000011 => 000000011
100000010 => 000000101 => 100000001
100000011 => 000000111 => 000000111
100000100 => 000001001 => 010000001
100000101 => 000001011 => 100000011
100000110 => 000001101 => 110000001
100000111 => 000001111 => 000001111
100001000 => 000010001 => 001000001
100001001 => 000010011 => 010000011
100001010 => 000010101 => 011000001
100001011 => 000010111 => 100000111
100001100 => 000011001 => 101000001
100001101 => 000011011 => 110000011
100001110 => 000011101 => 111000001
100001111 => 000011111 => 000011111
100010000 => 000100001 => 000100001
100010001 => 000100011 => 001000011
100010010 => 000100101 => 001100001
100010011 => 000100111 => 010000111
100010100 => 000101001 => 100100001
100010101 => 000101011 => 011000011
100010110 => 000101101 => 011100001
100010111 => 000101111 => 100001111
100011000 => 000110001 => 010100001
100011001 => 000110011 => 101000011
100011010 => 000110101 => 101100001
100011011 => 000110111 => 110000111
100011100 => 000111001 => 110100001
100011101 => 000111011 => 111000011
100011110 => 000111101 => 111100001
100011111 => 000111111 => 000111111
100100000 => 001000001 => 000010001
100100001 => 001000011 => 000100011
100100010 => 001000101 => 000110001
100100011 => 001000111 => 001000111
100100100 => 001001001 => 100010001
100100101 => 001001011 => 001100011
100100110 => 001001101 => 001110001
100100111 => 001001111 => 010001111
100101000 => 001010001 => 010010001
100101001 => 001010011 => 100100011
100101010 => 001010101 => 100110001
100101011 => 001010111 => 011000111
100101100 => 001011001 => 110010001
100101101 => 001011011 => 011100011
100101110 => 001011101 => 011110001
100101111 => 001011111 => 100011111
100110000 => 001100001 => 001010001
100110001 => 001100011 => 010100011
100110010 => 001100101 => 010110001
100110011 => 001100111 => 101000111
100110100 => 001101001 => 011010001
100110101 => 001101011 => 101100011
100110110 => 001101101 => 101110001
100110111 => 001101111 => 110001111
100111000 => 001110001 => 101010001
100111001 => 001110011 => 110100011
100111010 => 001110101 => 110110001
100111011 => 001110111 => 111000111
100111100 => 001111001 => 111010001
100111101 => 001111011 => 111100011
100111110 => 001111101 => 111110001
100111111 => 001111111 => 001111111
101000000 => 010000001 => 000001001
101000001 => 010000011 => 000010011
101000010 => 010000101 => 000011001
101000011 => 010000111 => 000100111
101000100 => 010001001 => 100001001
101000101 => 010001011 => 000110011
101000110 => 010001101 => 000111001
101000111 => 010001111 => 001001111
101001000 => 010010001 => 010001001
101001001 => 010010011 => 100010011
101001010 => 010010101 => 100011001
101001011 => 010010111 => 001100111
101001100 => 010011001 => 110001001
101001101 => 010011011 => 001110011
101001110 => 010011101 => 001111001
101001111 => 010011111 => 010011111
101010000 => 010100001 => 001001001
101010001 => 010100011 => 010010011
101010010 => 010100101 => 010011001
101010011 => 010100111 => 100100111
101010100 => 010101001 => 011001001
101010101 => 010101011 => 100110011
101010110 => 010101101 => 100111001
101010111 => 010101111 => 011001111
101011000 => 010110001 => 101001001
101011001 => 010110011 => 110010011
101011010 => 010110101 => 110011001
101011011 => 010110111 => 011100111
101011100 => 010111001 => 111001001
101011101 => 010111011 => 011110011
101011110 => 010111101 => 011111001
101011111 => 010111111 => 100111111
101100000 => 011000001 => 000101001
101100001 => 011000011 => 001010011
101100010 => 011000101 => 001011001
101100011 => 011000111 => 010100111
101100100 => 011001001 => 001101001
101100101 => 011001011 => 010110011
101100110 => 011001101 => 010111001
101100111 => 011001111 => 101001111
101101000 => 011010001 => 100101001
101101001 => 011010011 => 011010011
101101010 => 011010101 => 011011001
101101011 => 011010111 => 101100111
101101100 => 011011001 => 011101001
101101101 => 011011011 => 101110011
101101110 => 011011101 => 101111001
101101111 => 011011111 => 110011111
101110000 => 011100001 => 010101001
101110001 => 011100011 => 101010011
101110010 => 011100101 => 101011001
101110011 => 011100111 => 110100111
101110100 => 011101001 => 101101001
101110101 => 011101011 => 110110011
101110110 => 011101101 => 110111001
101110111 => 011101111 => 111001111
101111000 => 011110001 => 110101001
101111001 => 011110011 => 111010011
101111010 => 011110101 => 111011001
101111011 => 011110111 => 111100111
101111100 => 011111001 => 111101001
101111101 => 011111011 => 111110011
101111110 => 011111101 => 111111001
101111111 => 011111111 => 011111111
110000000 => 100000001 => 000000101
110000001 => 100000011 => 000001011
110000010 => 100000101 => 000001101
110000011 => 100000111 => 000010111
110000100 => 100001001 => 100000101
110000101 => 100001011 => 000011011
110000110 => 100001101 => 000011101
110000111 => 100001111 => 000101111
110001000 => 100010001 => 010000101
110001001 => 100010011 => 100001011
110001010 => 100010101 => 100001101
110001011 => 100010111 => 000110111
110001100 => 100011001 => 110000101
110001101 => 100011011 => 000111011
110001110 => 100011101 => 000111101
110001111 => 100011111 => 001011111
110010000 => 100100001 => 001000101
110010001 => 100100011 => 010001011
110010010 => 100100101 => 010001101
110010011 => 100100111 => 100010111
110010100 => 100101001 => 011000101
110010101 => 100101011 => 100011011
110010110 => 100101101 => 100011101
110010111 => 100101111 => 001101111
110011000 => 100110001 => 101000101
110011001 => 100110011 => 110001011
110011010 => 100110101 => 110001101
110011011 => 100110111 => 001110111
110011100 => 100111001 => 111000101
110011101 => 100111011 => 001111011
110011110 => 100111101 => 001111101
110011111 => 100111111 => 010111111
110100000 => 101000001 => 000100101
110100001 => 101000011 => 001001011
110100010 => 101000101 => 001001101
110100011 => 101000111 => 010010111
110100100 => 101001001 => 001100101
110100101 => 101001011 => 010011011
110100110 => 101001101 => 010011101
110100111 => 101001111 => 100101111
110101000 => 101010001 => 100100101
110101001 => 101010011 => 011001011
110101010 => 101010101 => 011001101
110101011 => 101010111 => 100110111
110101100 => 101011001 => 011100101
110101101 => 101011011 => 100111011
110101110 => 101011101 => 100111101
110101111 => 101011111 => 011011111
110110000 => 101100001 => 010100101
110110001 => 101100011 => 101001011
110110010 => 101100101 => 101001101
110110011 => 101100111 => 110010111
110110100 => 101101001 => 101100101
110110101 => 101101011 => 110011011
110110110 => 101101101 => 110011101
110110111 => 101101111 => 011101111
110111000 => 101110001 => 110100101
110111001 => 101110011 => 111001011
110111010 => 101110101 => 111001101
110111011 => 101110111 => 011110111
110111100 => 101111001 => 111100101
110111101 => 101111011 => 011111011
110111110 => 101111101 => 011111101
110111111 => 101111111 => 101111111
111000000 => 110000001 => 000010101
111000001 => 110000011 => 000101011
111000010 => 110000101 => 000101101
111000011 => 110000111 => 001010111
111000100 => 110001001 => 000110101
111000101 => 110001011 => 001011011
111000110 => 110001101 => 001011101
111000111 => 110001111 => 010101111
111001000 => 110010001 => 100010101
111001001 => 110010011 => 001101011
111001010 => 110010101 => 001101101
111001011 => 110010111 => 010110111
111001100 => 110011001 => 001110101
111001101 => 110011011 => 010111011
111001110 => 110011101 => 010111101
111001111 => 110011111 => 101011111
111010000 => 110100001 => 010010101
111010001 => 110100011 => 100101011
111010010 => 110100101 => 100101101
111010011 => 110100111 => 011010111
111010100 => 110101001 => 100110101
111010101 => 110101011 => 011011011
111010110 => 110101101 => 011011101
111010111 => 110101111 => 101101111
111011000 => 110110001 => 110010101
111011001 => 110110011 => 011101011
111011010 => 110110101 => 011101101
111011011 => 110110111 => 101110111
111011100 => 110111001 => 011110101
111011101 => 110111011 => 101111011
111011110 => 110111101 => 101111101
111011111 => 110111111 => 110111111
111100000 => 111000001 => 001010101
111100001 => 111000011 => 010101011
111100010 => 111000101 => 010101101
111100011 => 111000111 => 101010111
111100100 => 111001001 => 010110101
111100101 => 111001011 => 101011011
111100110 => 111001101 => 101011101
111100111 => 111001111 => 110101111
111101000 => 111010001 => 011010101
111101001 => 111010011 => 101101011
111101010 => 111010101 => 101101101
111101011 => 111010111 => 110110111
111101100 => 111011001 => 101110101
111101101 => 111011011 => 110111011
111101110 => 111011101 => 110111101
111101111 => 111011111 => 111011111
111110000 => 111100001 => 101010101
111110001 => 111100011 => 110101011
111110010 => 111100101 => 110101101
111110011 => 111100111 => 111010111
111110100 => 111101001 => 110110101
111110101 => 111101011 => 111011011
111110110 => 111101101 => 111011101
111110111 => 111101111 => 111101111
111111000 => 111110001 => 111010101
111111001 => 111110011 => 111101011
111111010 => 111110101 => 111101101
111111011 => 111110111 => 111110111
111111100 => 111111001 => 111110101
111111101 => 111111011 => 111111011
111111110 => 111111101 => 111111101
111111111 => 111111111 => 111111111
1011101000 => 0111010001 => 0110101001
1011110000 => 0111100001 => 1010101001
1011111111 => 0111111111 => 0111111111
1011111110 => 0111111101 => 1111111001
1011111101 => 0111111011 => 1111110011
1011110100 => 0111101001 => 1101101001
1011100000 => 0111000001 => 0010101001
1011010000 => 0110100001 => 0100101001
1001000000 => 0010000001 => 0000010001
1000000000 => 0000000001 => 0000000001
10000000000 => 00000000001 => 00000000001
10111111110 => 01111111101 => 11111111001
0111111111 => 1111111110 => 1111111110
0100000001 => 1000000010 => 0000000110
01111111111 => 11111111110 => 11111111110
01000000001 => 10000000010 => 00000000110
0100010111 => 1000101110 => 1000011110
0100001111 => 1000011110 => 0000111110
0100000010 => 1000000100 => 1000000010
0100000000 => 1000000000 => 0000000010
0101111111 => 1011111110 => 0111111110
01000000000 => 10000000000 => 00000000010
0100001011 => 1000010110 => 1000001110
0100101111 => 1001011110 => 1000111110
0101011111 => 1010111110 => 1001111110
0110111111 => 1101111110 => 1011111110
10111111111 => 01111111111 => 01111111111
Map
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.