Identifier
Mp00136: Binary words —rotate back-to-front⟶ 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 => 100 => 010
010 => 001 => 001
011 => 101 => 101
100 => 010 => 100
101 => 110 => 110
110 => 011 => 011
111 => 111 => 111
0000 => 0000 => 0000
0001 => 1000 => 0010
0010 => 0001 => 0001
0011 => 1001 => 0101
0100 => 0010 => 1000
0101 => 1010 => 0110
0110 => 0011 => 0011
0111 => 1011 => 1011
1000 => 0100 => 0100
1001 => 1100 => 1010
1010 => 0101 => 1001
1011 => 1101 => 1101
1100 => 0110 => 1100
1101 => 1110 => 1110
1110 => 0111 => 0111
1111 => 1111 => 1111
00000 => 00000 => 00000
00001 => 10000 => 00010
00010 => 00001 => 00001
00011 => 10001 => 00101
00100 => 00010 => 10000
00101 => 10010 => 00110
00110 => 00011 => 00011
00111 => 10011 => 01011
01000 => 00100 => 01000
01001 => 10100 => 10010
01010 => 00101 => 10001
01011 => 10101 => 01101
01100 => 00110 => 11000
01101 => 10110 => 01110
01110 => 00111 => 00111
01111 => 10111 => 10111
10000 => 01000 => 00100
10001 => 11000 => 01010
10010 => 01001 => 01001
10011 => 11001 => 10101
10100 => 01010 => 01100
10101 => 11010 => 10110
10110 => 01011 => 10011
10111 => 11011 => 11011
11000 => 01100 => 10100
11001 => 11100 => 11010
11010 => 01101 => 11001
11011 => 11101 => 11101
11100 => 01110 => 11100
11101 => 11110 => 11110
11110 => 01111 => 01111
11111 => 11111 => 11111
000000 => 000000 => 000000
000001 => 100000 => 000010
000010 => 000001 => 000001
000011 => 100001 => 000101
000100 => 000010 => 100000
000101 => 100010 => 000110
000110 => 000011 => 000011
000111 => 100011 => 001011
001000 => 000100 => 010000
001001 => 100100 => 100010
001010 => 000101 => 100001
001011 => 100101 => 001101
001100 => 000110 => 110000
001101 => 100110 => 001110
001110 => 000111 => 000111
001111 => 100111 => 010111
010000 => 001000 => 001000
010001 => 101000 => 010010
010010 => 001001 => 010001
010011 => 101001 => 100101
010100 => 001010 => 011000
010101 => 101010 => 100110
010110 => 001011 => 100011
010111 => 101011 => 011011
011000 => 001100 => 101000
011001 => 101100 => 110010
011010 => 001101 => 110001
011011 => 101101 => 011101
011100 => 001110 => 111000
011101 => 101110 => 011110
011110 => 001111 => 001111
011111 => 101111 => 101111
100000 => 010000 => 000100
100001 => 110000 => 001010
100010 => 010001 => 001001
100011 => 110001 => 010101
100100 => 010010 => 001100
100101 => 110010 => 010110
100110 => 010011 => 010011
>>> Load all 1055 entries. <<<
100111 => 110011 => 101011
101000 => 010100 => 100100
101001 => 110100 => 011010
101010 => 010101 => 011001
101011 => 110101 => 101101
101100 => 010110 => 011100
101101 => 110110 => 101110
101110 => 010111 => 100111
101111 => 110111 => 110111
110000 => 011000 => 010100
110001 => 111000 => 101010
110010 => 011001 => 101001
110011 => 111001 => 110101
110100 => 011010 => 101100
110101 => 111010 => 110110
110110 => 011011 => 110011
110111 => 111011 => 111011
111000 => 011100 => 110100
111001 => 111100 => 111010
111010 => 011101 => 111001
111011 => 111101 => 111101
111100 => 011110 => 111100
111101 => 111110 => 111110
111110 => 011111 => 011111
111111 => 111111 => 111111
0000000 => 0000000 => 0000000
0000001 => 1000000 => 0000010
0000010 => 0000001 => 0000001
0000011 => 1000001 => 0000101
0000100 => 0000010 => 1000000
0000101 => 1000010 => 0000110
0000110 => 0000011 => 0000011
0000111 => 1000011 => 0001011
0001000 => 0000100 => 0100000
0001001 => 1000100 => 1000010
0001010 => 0000101 => 1000001
0001011 => 1000101 => 0001101
0001100 => 0000110 => 1100000
0001101 => 1000110 => 0001110
0001110 => 0000111 => 0000111
0001111 => 1000111 => 0010111
0010000 => 0001000 => 0010000
0010001 => 1001000 => 0100010
0010010 => 0001001 => 0100001
0010011 => 1001001 => 1000101
0010100 => 0001010 => 0110000
0010101 => 1001010 => 1000110
0010110 => 0001011 => 1000011
0010111 => 1001011 => 0011011
0011000 => 0001100 => 1010000
0011001 => 1001100 => 1100010
0011010 => 0001101 => 1100001
0011011 => 1001101 => 0011101
0011100 => 0001110 => 1110000
0011101 => 1001110 => 0011110
0011110 => 0001111 => 0001111
0011111 => 1001111 => 0101111
0100000 => 0010000 => 0001000
0100001 => 1010000 => 0010010
0100010 => 0010001 => 0010001
0100011 => 1010001 => 0100101
0100100 => 0010010 => 0011000
0100101 => 1010010 => 0100110
0100110 => 0010011 => 0100011
0100111 => 1010011 => 1001011
0101000 => 0010100 => 1001000
0101001 => 1010100 => 0110010
0101010 => 0010101 => 0110001
0101011 => 1010101 => 1001101
0101100 => 0010110 => 0111000
0101101 => 1010110 => 1001110
0101110 => 0010111 => 1000111
0101111 => 1010111 => 0110111
0110000 => 0011000 => 0101000
0110001 => 1011000 => 1010010
0110010 => 0011001 => 1010001
0110011 => 1011001 => 1100101
0110100 => 0011010 => 1011000
0110101 => 1011010 => 1100110
0110110 => 0011011 => 1100011
0110111 => 1011011 => 0111011
0111000 => 0011100 => 1101000
0111001 => 1011100 => 1110010
0111010 => 0011101 => 1110001
0111011 => 1011101 => 0111101
0111100 => 0011110 => 1111000
0111101 => 1011110 => 0111110
0111110 => 0011111 => 0011111
0111111 => 1011111 => 1011111
1000000 => 0100000 => 0000100
1000001 => 1100000 => 0001010
1000010 => 0100001 => 0001001
1000011 => 1100001 => 0010101
1000100 => 0100010 => 0001100
1000101 => 1100010 => 0010110
1000110 => 0100011 => 0010011
1000111 => 1100011 => 0101011
1001000 => 0100100 => 1000100
1001001 => 1100100 => 0011010
1001010 => 0100101 => 0011001
1001011 => 1100101 => 0101101
1001100 => 0100110 => 0011100
1001101 => 1100110 => 0101110
1001110 => 0100111 => 0100111
1001111 => 1100111 => 1010111
1010000 => 0101000 => 0100100
1010001 => 1101000 => 1001010
1010010 => 0101001 => 1001001
1010011 => 1101001 => 0110101
1010100 => 0101010 => 1001100
1010101 => 1101010 => 0110110
1010110 => 0101011 => 0110011
1010111 => 1101011 => 1011011
1011000 => 0101100 => 1100100
1011001 => 1101100 => 0111010
1011010 => 0101101 => 0111001
1011011 => 1101101 => 1011101
1011100 => 0101110 => 0111100
1011101 => 1101110 => 1011110
1011110 => 0101111 => 1001111
1011111 => 1101111 => 1101111
1100000 => 0110000 => 0010100
1100001 => 1110000 => 0101010
1100010 => 0110001 => 0101001
1100011 => 1110001 => 1010101
1100100 => 0110010 => 0101100
1100101 => 1110010 => 1010110
1100110 => 0110011 => 1010011
1100111 => 1110011 => 1101011
1101000 => 0110100 => 0110100
1101001 => 1110100 => 1011010
1101010 => 0110101 => 1011001
1101011 => 1110101 => 1101101
1101100 => 0110110 => 1011100
1101101 => 1110110 => 1101110
1101110 => 0110111 => 1100111
1101111 => 1110111 => 1110111
1110000 => 0111000 => 1010100
1110001 => 1111000 => 1101010
1110010 => 0111001 => 1101001
1110011 => 1111001 => 1110101
1110100 => 0111010 => 1101100
1110101 => 1111010 => 1110110
1110110 => 0111011 => 1110011
1110111 => 1111011 => 1111011
1111000 => 0111100 => 1110100
1111001 => 1111100 => 1111010
1111010 => 0111101 => 1111001
1111011 => 1111101 => 1111101
1111100 => 0111110 => 1111100
1111101 => 1111110 => 1111110
1111110 => 0111111 => 0111111
1111111 => 1111111 => 1111111
00000000 => 00000000 => 00000000
00000001 => 10000000 => 00000010
00000010 => 00000001 => 00000001
00000011 => 10000001 => 00000101
00000100 => 00000010 => 10000000
00000101 => 10000010 => 00000110
00000110 => 00000011 => 00000011
00000111 => 10000011 => 00001011
00001000 => 00000100 => 01000000
00001001 => 10000100 => 10000010
00001010 => 00000101 => 10000001
00001011 => 10000101 => 00001101
00001100 => 00000110 => 11000000
00001101 => 10000110 => 00001110
00001110 => 00000111 => 00000111
00001111 => 10000111 => 00010111
00010000 => 00001000 => 00100000
00010001 => 10001000 => 01000010
00010010 => 00001001 => 01000001
00010011 => 10001001 => 10000101
00010100 => 00001010 => 01100000
00010101 => 10001010 => 10000110
00010110 => 00001011 => 10000011
00010111 => 10001011 => 00011011
00011000 => 00001100 => 10100000
00011001 => 10001100 => 11000010
00011010 => 00001101 => 11000001
00011011 => 10001101 => 00011101
00011100 => 00001110 => 11100000
00011101 => 10001110 => 00011110
00011110 => 00001111 => 00001111
00011111 => 10001111 => 00101111
00100000 => 00010000 => 00010000
00100001 => 10010000 => 00100010
00100010 => 00010001 => 00100001
00100011 => 10010001 => 01000101
00100100 => 00010010 => 00110000
00100101 => 10010010 => 01000110
00100110 => 00010011 => 01000011
00100111 => 10010011 => 10001011
00101000 => 00010100 => 10010000
00101001 => 10010100 => 01100010
00101010 => 00010101 => 01100001
00101011 => 10010101 => 10001101
00101100 => 00010110 => 01110000
00101101 => 10010110 => 10001110
00101110 => 00010111 => 10000111
00101111 => 10010111 => 00110111
00110000 => 00011000 => 01010000
00110001 => 10011000 => 10100010
00110010 => 00011001 => 10100001
00110011 => 10011001 => 11000101
00110100 => 00011010 => 10110000
00110101 => 10011010 => 11000110
00110110 => 00011011 => 11000011
00110111 => 10011011 => 00111011
00111000 => 00011100 => 11010000
00111001 => 10011100 => 11100010
00111010 => 00011101 => 11100001
00111011 => 10011101 => 00111101
00111100 => 00011110 => 11110000
00111101 => 10011110 => 00111110
00111110 => 00011111 => 00011111
00111111 => 10011111 => 01011111
01000000 => 00100000 => 00001000
01000001 => 10100000 => 00010010
01000010 => 00100001 => 00010001
01000011 => 10100001 => 00100101
01000100 => 00100010 => 00011000
01000101 => 10100010 => 00100110
01000110 => 00100011 => 00100011
01000111 => 10100011 => 01001011
01001000 => 00100100 => 10001000
01001001 => 10100100 => 00110010
01001010 => 00100101 => 00110001
01001011 => 10100101 => 01001101
01001100 => 00100110 => 00111000
01001101 => 10100110 => 01001110
01001110 => 00100111 => 01000111
01001111 => 10100111 => 10010111
01010000 => 00101000 => 01001000
01010001 => 10101000 => 10010010
01010010 => 00101001 => 10010001
01010011 => 10101001 => 01100101
01010100 => 00101010 => 10011000
01010101 => 10101010 => 01100110
01010110 => 00101011 => 01100011
01010111 => 10101011 => 10011011
01011000 => 00101100 => 11001000
01011001 => 10101100 => 01110010
01011010 => 00101101 => 01110001
01011011 => 10101101 => 10011101
01011100 => 00101110 => 01111000
01011101 => 10101110 => 10011110
01011110 => 00101111 => 10001111
01011111 => 10101111 => 01101111
01100000 => 00110000 => 00101000
01100001 => 10110000 => 01010010
01100010 => 00110001 => 01010001
01100011 => 10110001 => 10100101
01100100 => 00110010 => 01011000
01100101 => 10110010 => 10100110
01100110 => 00110011 => 10100011
01100111 => 10110011 => 11001011
01101000 => 00110100 => 01101000
01101001 => 10110100 => 10110010
01101010 => 00110101 => 10110001
01101011 => 10110101 => 11001101
01101100 => 00110110 => 10111000
01101101 => 10110110 => 11001110
01101110 => 00110111 => 11000111
01101111 => 10110111 => 01110111
01110000 => 00111000 => 10101000
01110001 => 10111000 => 11010010
01110010 => 00111001 => 11010001
01110011 => 10111001 => 11100101
01110100 => 00111010 => 11011000
01110101 => 10111010 => 11100110
01110110 => 00111011 => 11100011
01110111 => 10111011 => 01111011
01111000 => 00111100 => 11101000
01111001 => 10111100 => 11110010
01111010 => 00111101 => 11110001
01111011 => 10111101 => 01111101
01111100 => 00111110 => 11111000
01111101 => 10111110 => 01111110
01111110 => 00111111 => 00111111
01111111 => 10111111 => 10111111
10000000 => 01000000 => 00000100
10000001 => 11000000 => 00001010
10000010 => 01000001 => 00001001
10000011 => 11000001 => 00010101
10000100 => 01000010 => 00001100
10000101 => 11000010 => 00010110
10000110 => 01000011 => 00010011
10000111 => 11000011 => 00101011
10001000 => 01000100 => 10000100
10001001 => 11000100 => 00011010
10001010 => 01000101 => 00011001
10001011 => 11000101 => 00101101
10001100 => 01000110 => 00011100
10001101 => 11000110 => 00101110
10001110 => 01000111 => 00100111
10001111 => 11000111 => 01010111
10010000 => 01001000 => 01000100
10010001 => 11001000 => 10001010
10010010 => 01001001 => 10001001
10010011 => 11001001 => 00110101
10010100 => 01001010 => 10001100
10010101 => 11001010 => 00110110
10010110 => 01001011 => 00110011
10010111 => 11001011 => 01011011
10011000 => 01001100 => 11000100
10011001 => 11001100 => 00111010
10011010 => 01001101 => 00111001
10011011 => 11001101 => 01011101
10011100 => 01001110 => 00111100
10011101 => 11001110 => 01011110
10011110 => 01001111 => 01001111
10011111 => 11001111 => 10101111
10100000 => 01010000 => 00100100
10100001 => 11010000 => 01001010
10100010 => 01010001 => 01001001
10100011 => 11010001 => 10010101
10100100 => 01010010 => 01001100
10100101 => 11010010 => 10010110
10100110 => 01010011 => 10010011
10100111 => 11010011 => 01101011
10101000 => 01010100 => 01100100
10101001 => 11010100 => 10011010
10101010 => 01010101 => 10011001
10101011 => 11010101 => 01101101
10101100 => 01010110 => 10011100
10101101 => 11010110 => 01101110
10101110 => 01010111 => 01100111
10101111 => 11010111 => 10110111
10110000 => 01011000 => 10100100
10110001 => 11011000 => 11001010
10110010 => 01011001 => 11001001
10110011 => 11011001 => 01110101
10110100 => 01011010 => 11001100
10110101 => 11011010 => 01110110
10110110 => 01011011 => 01110011
10110111 => 11011011 => 10111011
10111000 => 01011100 => 11100100
10111001 => 11011100 => 01111010
10111010 => 01011101 => 01111001
10111011 => 11011101 => 10111101
10111100 => 01011110 => 01111100
10111101 => 11011110 => 10111110
10111110 => 01011111 => 10011111
10111111 => 11011111 => 11011111
11000000 => 01100000 => 00010100
11000001 => 11100000 => 00101010
11000010 => 01100001 => 00101001
11000011 => 11100001 => 01010101
11000100 => 01100010 => 00101100
11000101 => 11100010 => 01010110
11000110 => 01100011 => 01010011
11000111 => 11100011 => 10101011
11001000 => 01100100 => 00110100
11001001 => 11100100 => 01011010
11001010 => 01100101 => 01011001
11001011 => 11100101 => 10101101
11001100 => 01100110 => 01011100
11001101 => 11100110 => 10101110
11001110 => 01100111 => 10100111
11001111 => 11100111 => 11010111
11010000 => 01101000 => 10010100
11010001 => 11101000 => 01101010
11010010 => 01101001 => 01101001
11010011 => 11101001 => 10110101
11010100 => 01101010 => 01101100
11010101 => 11101010 => 10110110
11010110 => 01101011 => 10110011
11010111 => 11101011 => 11011011
11011000 => 01101100 => 01110100
11011001 => 11101100 => 10111010
11011010 => 01101101 => 10111001
11011011 => 11101101 => 11011101
11011100 => 01101110 => 10111100
11011101 => 11101110 => 11011110
11011110 => 01101111 => 11001111
11011111 => 11101111 => 11101111
11100000 => 01110000 => 01010100
11100001 => 11110000 => 10101010
11100010 => 01110001 => 10101001
11100011 => 11110001 => 11010101
11100100 => 01110010 => 10101100
11100101 => 11110010 => 11010110
11100110 => 01110011 => 11010011
11100111 => 11110011 => 11101011
11101000 => 01110100 => 10110100
11101001 => 11110100 => 11011010
11101010 => 01110101 => 11011001
11101011 => 11110101 => 11101101
11101100 => 01110110 => 11011100
11101101 => 11110110 => 11101110
11101110 => 01110111 => 11100111
11101111 => 11110111 => 11110111
11110000 => 01111000 => 11010100
11110001 => 11111000 => 11101010
11110010 => 01111001 => 11101001
11110011 => 11111001 => 11110101
11110100 => 01111010 => 11101100
11110101 => 11111010 => 11110110
11110110 => 01111011 => 11110011
11110111 => 11111011 => 11111011
11111000 => 01111100 => 11110100
11111001 => 11111100 => 11111010
11111010 => 01111101 => 11111001
11111011 => 11111101 => 11111101
11111100 => 01111110 => 11111100
11111101 => 11111110 => 11111110
11111110 => 01111111 => 01111111
11111111 => 11111111 => 11111111
000000000 => 000000000 => 000000000
000000001 => 100000000 => 000000010
000000010 => 000000001 => 000000001
000000011 => 100000001 => 000000101
000000100 => 000000010 => 100000000
000000101 => 100000010 => 000000110
000000110 => 000000011 => 000000011
000000111 => 100000011 => 000001011
000001000 => 000000100 => 010000000
000001001 => 100000100 => 100000010
000001010 => 000000101 => 100000001
000001011 => 100000101 => 000001101
000001100 => 000000110 => 110000000
000001101 => 100000110 => 000001110
000001110 => 000000111 => 000000111
000001111 => 100000111 => 000010111
000010000 => 000001000 => 001000000
000010001 => 100001000 => 010000010
000010010 => 000001001 => 010000001
000010011 => 100001001 => 100000101
000010100 => 000001010 => 011000000
000010101 => 100001010 => 100000110
000010110 => 000001011 => 100000011
000010111 => 100001011 => 000011011
000011000 => 000001100 => 101000000
000011001 => 100001100 => 110000010
000011010 => 000001101 => 110000001
000011011 => 100001101 => 000011101
000011100 => 000001110 => 111000000
000011101 => 100001110 => 000011110
000011110 => 000001111 => 000001111
000011111 => 100001111 => 000101111
000100000 => 000010000 => 000100000
000100001 => 100010000 => 001000010
000100010 => 000010001 => 001000001
000100011 => 100010001 => 010000101
000100100 => 000010010 => 001100000
000100101 => 100010010 => 010000110
000100110 => 000010011 => 010000011
000100111 => 100010011 => 100001011
000101000 => 000010100 => 100100000
000101001 => 100010100 => 011000010
000101010 => 000010101 => 011000001
000101011 => 100010101 => 100001101
000101100 => 000010110 => 011100000
000101101 => 100010110 => 100001110
000101110 => 000010111 => 100000111
000101111 => 100010111 => 000110111
000110000 => 000011000 => 010100000
000110001 => 100011000 => 101000010
000110010 => 000011001 => 101000001
000110011 => 100011001 => 110000101
000110100 => 000011010 => 101100000
000110101 => 100011010 => 110000110
000110110 => 000011011 => 110000011
000110111 => 100011011 => 000111011
000111000 => 000011100 => 110100000
000111001 => 100011100 => 111000010
000111010 => 000011101 => 111000001
000111011 => 100011101 => 000111101
000111100 => 000011110 => 111100000
000111101 => 100011110 => 000111110
000111110 => 000011111 => 000011111
000111111 => 100011111 => 001011111
001000000 => 000100000 => 000010000
001000001 => 100100000 => 000100010
001000010 => 000100001 => 000100001
001000011 => 100100001 => 001000101
001000100 => 000100010 => 000110000
001000101 => 100100010 => 001000110
001000110 => 000100011 => 001000011
001000111 => 100100011 => 010001011
001001000 => 000100100 => 100010000
001001001 => 100100100 => 001100010
001001010 => 000100101 => 001100001
001001011 => 100100101 => 010001101
001001100 => 000100110 => 001110000
001001101 => 100100110 => 010001110
001001110 => 000100111 => 010000111
001001111 => 100100111 => 100010111
001010000 => 000101000 => 010010000
001010001 => 100101000 => 100100010
001010010 => 000101001 => 100100001
001010011 => 100101001 => 011000101
001010100 => 000101010 => 100110000
001010101 => 100101010 => 011000110
001010110 => 000101011 => 011000011
001010111 => 100101011 => 100011011
001011000 => 000101100 => 110010000
001011001 => 100101100 => 011100010
001011010 => 000101101 => 011100001
001011011 => 100101101 => 100011101
001011100 => 000101110 => 011110000
001011101 => 100101110 => 100011110
001011110 => 000101111 => 100001111
001011111 => 100101111 => 001101111
001100000 => 000110000 => 001010000
001100001 => 100110000 => 010100010
001100010 => 000110001 => 010100001
001100011 => 100110001 => 101000101
001100100 => 000110010 => 010110000
001100101 => 100110010 => 101000110
001100110 => 000110011 => 101000011
001100111 => 100110011 => 110001011
001101000 => 000110100 => 011010000
001101001 => 100110100 => 101100010
001101010 => 000110101 => 101100001
001101011 => 100110101 => 110001101
001101100 => 000110110 => 101110000
001101101 => 100110110 => 110001110
001101110 => 000110111 => 110000111
001101111 => 100110111 => 001110111
001110000 => 000111000 => 101010000
001110001 => 100111000 => 110100010
001110010 => 000111001 => 110100001
001110011 => 100111001 => 111000101
001110100 => 000111010 => 110110000
001110101 => 100111010 => 111000110
001110110 => 000111011 => 111000011
001110111 => 100111011 => 001111011
001111000 => 000111100 => 111010000
001111001 => 100111100 => 111100010
001111010 => 000111101 => 111100001
001111011 => 100111101 => 001111101
001111100 => 000111110 => 111110000
001111101 => 100111110 => 001111110
001111110 => 000111111 => 000111111
001111111 => 100111111 => 010111111
010000000 => 001000000 => 000001000
010000001 => 101000000 => 000010010
010000010 => 001000001 => 000010001
010000011 => 101000001 => 000100101
010000100 => 001000010 => 000011000
010000101 => 101000010 => 000100110
010000110 => 001000011 => 000100011
010000111 => 101000011 => 001001011
010001000 => 001000100 => 100001000
010001001 => 101000100 => 000110010
010001010 => 001000101 => 000110001
010001011 => 101000101 => 001001101
010001100 => 001000110 => 000111000
010001101 => 101000110 => 001001110
010001110 => 001000111 => 001000111
010001111 => 101000111 => 010010111
010010000 => 001001000 => 010001000
010010001 => 101001000 => 100010010
010010010 => 001001001 => 100010001
010010011 => 101001001 => 001100101
010010100 => 001001010 => 100011000
010010101 => 101001010 => 001100110
010010110 => 001001011 => 001100011
010010111 => 101001011 => 010011011
010011000 => 001001100 => 110001000
010011001 => 101001100 => 001110010
010011010 => 001001101 => 001110001
010011011 => 101001101 => 010011101
010011100 => 001001110 => 001111000
010011101 => 101001110 => 010011110
010011110 => 001001111 => 010001111
010011111 => 101001111 => 100101111
010100000 => 001010000 => 001001000
010100001 => 101010000 => 010010010
010100010 => 001010001 => 010010001
010100011 => 101010001 => 100100101
010100100 => 001010010 => 010011000
010100101 => 101010010 => 100100110
010100110 => 001010011 => 100100011
010100111 => 101010011 => 011001011
010101000 => 001010100 => 011001000
010101001 => 101010100 => 100110010
010101010 => 001010101 => 100110001
010101011 => 101010101 => 011001101
010101100 => 001010110 => 100111000
010101101 => 101010110 => 011001110
010101110 => 001010111 => 011000111
010101111 => 101010111 => 100110111
010110000 => 001011000 => 101001000
010110001 => 101011000 => 110010010
010110010 => 001011001 => 110010001
010110011 => 101011001 => 011100101
010110100 => 001011010 => 110011000
010110101 => 101011010 => 011100110
010110110 => 001011011 => 011100011
010110111 => 101011011 => 100111011
010111000 => 001011100 => 111001000
010111001 => 101011100 => 011110010
010111010 => 001011101 => 011110001
010111011 => 101011101 => 100111101
010111100 => 001011110 => 011111000
010111101 => 101011110 => 100111110
010111110 => 001011111 => 100011111
010111111 => 101011111 => 011011111
011000000 => 001100000 => 000101000
011000001 => 101100000 => 001010010
011000010 => 001100001 => 001010001
011000011 => 101100001 => 010100101
011000100 => 001100010 => 001011000
011000101 => 101100010 => 010100110
011000110 => 001100011 => 010100011
011000111 => 101100011 => 101001011
011001000 => 001100100 => 001101000
011001001 => 101100100 => 010110010
011001010 => 001100101 => 010110001
011001011 => 101100101 => 101001101
011001100 => 001100110 => 010111000
011001101 => 101100110 => 101001110
011001110 => 001100111 => 101000111
011001111 => 101100111 => 110010111
011010000 => 001101000 => 100101000
011010001 => 101101000 => 011010010
011010010 => 001101001 => 011010001
011010011 => 101101001 => 101100101
011010100 => 001101010 => 011011000
011010101 => 101101010 => 101100110
011010110 => 001101011 => 101100011
011010111 => 101101011 => 110011011
011011000 => 001101100 => 011101000
011011001 => 101101100 => 101110010
011011010 => 001101101 => 101110001
011011011 => 101101101 => 110011101
011011100 => 001101110 => 101111000
011011101 => 101101110 => 110011110
011011110 => 001101111 => 110001111
011011111 => 101101111 => 011101111
011100000 => 001110000 => 010101000
011100001 => 101110000 => 101010010
011100010 => 001110001 => 101010001
011100011 => 101110001 => 110100101
011100100 => 001110010 => 101011000
011100101 => 101110010 => 110100110
011100110 => 001110011 => 110100011
011100111 => 101110011 => 111001011
011101000 => 001110100 => 101101000
011101001 => 101110100 => 110110010
011101010 => 001110101 => 110110001
011101011 => 101110101 => 111001101
011101100 => 001110110 => 110111000
011101101 => 101110110 => 111001110
011101110 => 001110111 => 111000111
011101111 => 101110111 => 011110111
011110000 => 001111000 => 110101000
011110001 => 101111000 => 111010010
011110010 => 001111001 => 111010001
011110011 => 101111001 => 111100101
011110100 => 001111010 => 111011000
011110101 => 101111010 => 111100110
011110110 => 001111011 => 111100011
011110111 => 101111011 => 011111011
011111000 => 001111100 => 111101000
011111001 => 101111100 => 111110010
011111010 => 001111101 => 111110001
011111011 => 101111101 => 011111101
011111100 => 001111110 => 111111000
011111101 => 101111110 => 011111110
011111110 => 001111111 => 001111111
011111111 => 101111111 => 101111111
100000000 => 010000000 => 000000100
100000001 => 110000000 => 000001010
100000010 => 010000001 => 000001001
100000011 => 110000001 => 000010101
100000100 => 010000010 => 000001100
100000101 => 110000010 => 000010110
100000110 => 010000011 => 000010011
100000111 => 110000011 => 000101011
100001000 => 010000100 => 100000100
100001001 => 110000100 => 000011010
100001010 => 010000101 => 000011001
100001011 => 110000101 => 000101101
100001100 => 010000110 => 000011100
100001101 => 110000110 => 000101110
100001110 => 010000111 => 000100111
100001111 => 110000111 => 001010111
100010000 => 010001000 => 010000100
100010001 => 110001000 => 100001010
100010010 => 010001001 => 100001001
100010011 => 110001001 => 000110101
100010100 => 010001010 => 100001100
100010101 => 110001010 => 000110110
100010110 => 010001011 => 000110011
100010111 => 110001011 => 001011011
100011000 => 010001100 => 110000100
100011001 => 110001100 => 000111010
100011010 => 010001101 => 000111001
100011011 => 110001101 => 001011101
100011100 => 010001110 => 000111100
100011101 => 110001110 => 001011110
100011110 => 010001111 => 001001111
100011111 => 110001111 => 010101111
100100000 => 010010000 => 001000100
100100001 => 110010000 => 010001010
100100010 => 010010001 => 010001001
100100011 => 110010001 => 100010101
100100100 => 010010010 => 010001100
100100101 => 110010010 => 100010110
100100110 => 010010011 => 100010011
100100111 => 110010011 => 001101011
100101000 => 010010100 => 011000100
100101001 => 110010100 => 100011010
100101010 => 010010101 => 100011001
100101011 => 110010101 => 001101101
100101100 => 010010110 => 100011100
100101101 => 110010110 => 001101110
100101110 => 010010111 => 001100111
100101111 => 110010111 => 010110111
100110000 => 010011000 => 101000100
100110001 => 110011000 => 110001010
100110010 => 010011001 => 110001001
100110011 => 110011001 => 001110101
100110100 => 010011010 => 110001100
100110101 => 110011010 => 001110110
100110110 => 010011011 => 001110011
100110111 => 110011011 => 010111011
100111000 => 010011100 => 111000100
100111001 => 110011100 => 001111010
100111010 => 010011101 => 001111001
100111011 => 110011101 => 010111101
100111100 => 010011110 => 001111100
100111101 => 110011110 => 010111110
100111110 => 010011111 => 010011111
100111111 => 110011111 => 101011111
101000000 => 010100000 => 000100100
101000001 => 110100000 => 001001010
101000010 => 010100001 => 001001001
101000011 => 110100001 => 010010101
101000100 => 010100010 => 001001100
101000101 => 110100010 => 010010110
101000110 => 010100011 => 010010011
101000111 => 110100011 => 100101011
101001000 => 010100100 => 001100100
101001001 => 110100100 => 010011010
101001010 => 010100101 => 010011001
101001011 => 110100101 => 100101101
101001100 => 010100110 => 010011100
101001101 => 110100110 => 100101110
101001110 => 010100111 => 100100111
101001111 => 110100111 => 011010111
101010000 => 010101000 => 100100100
101010001 => 110101000 => 011001010
101010010 => 010101001 => 011001001
101010011 => 110101001 => 100110101
101010100 => 010101010 => 011001100
101010101 => 110101010 => 100110110
101010110 => 010101011 => 100110011
101010111 => 110101011 => 011011011
101011000 => 010101100 => 011100100
101011001 => 110101100 => 100111010
101011010 => 010101101 => 100111001
101011011 => 110101101 => 011011101
101011100 => 010101110 => 100111100
101011101 => 110101110 => 011011110
101011110 => 010101111 => 011001111
101011111 => 110101111 => 101101111
101100000 => 010110000 => 010100100
101100001 => 110110000 => 101001010
101100010 => 010110001 => 101001001
101100011 => 110110001 => 110010101
101100100 => 010110010 => 101001100
101100101 => 110110010 => 110010110
101100110 => 010110011 => 110010011
101100111 => 110110011 => 011101011
101101000 => 010110100 => 101100100
101101001 => 110110100 => 110011010
101101010 => 010110101 => 110011001
101101011 => 110110101 => 011101101
101101100 => 010110110 => 110011100
101101101 => 110110110 => 011101110
101101110 => 010110111 => 011100111
101101111 => 110110111 => 101110111
101110000 => 010111000 => 110100100
101110001 => 110111000 => 111001010
101110010 => 010111001 => 111001001
101110011 => 110111001 => 011110101
101110100 => 010111010 => 111001100
101110101 => 110111010 => 011110110
101110110 => 010111011 => 011110011
101110111 => 110111011 => 101111011
101111000 => 010111100 => 111100100
101111001 => 110111100 => 011111010
101111010 => 010111101 => 011111001
101111011 => 110111101 => 101111101
101111100 => 010111110 => 011111100
101111101 => 110111110 => 101111110
101111110 => 010111111 => 100111111
101111111 => 110111111 => 110111111
110000000 => 011000000 => 000010100
110000001 => 111000000 => 000101010
110000010 => 011000001 => 000101001
110000011 => 111000001 => 001010101
110000100 => 011000010 => 000101100
110000101 => 111000010 => 001010110
110000110 => 011000011 => 001010011
110000111 => 111000011 => 010101011
110001000 => 011000100 => 000110100
110001001 => 111000100 => 001011010
110001010 => 011000101 => 001011001
110001011 => 111000101 => 010101101
110001100 => 011000110 => 001011100
110001101 => 111000110 => 010101110
110001110 => 011000111 => 010100111
110001111 => 111000111 => 101010111
110010000 => 011001000 => 100010100
110010001 => 111001000 => 001101010
110010010 => 011001001 => 001101001
110010011 => 111001001 => 010110101
110010100 => 011001010 => 001101100
110010101 => 111001010 => 010110110
110010110 => 011001011 => 010110011
110010111 => 111001011 => 101011011
110011000 => 011001100 => 001110100
110011001 => 111001100 => 010111010
110011010 => 011001101 => 010111001
110011011 => 111001101 => 101011101
110011100 => 011001110 => 010111100
110011101 => 111001110 => 101011110
110011110 => 011001111 => 101001111
110011111 => 111001111 => 110101111
110100000 => 011010000 => 010010100
110100001 => 111010000 => 100101010
110100010 => 011010001 => 100101001
110100011 => 111010001 => 011010101
110100100 => 011010010 => 100101100
110100101 => 111010010 => 011010110
110100110 => 011010011 => 011010011
110100111 => 111010011 => 101101011
110101000 => 011010100 => 100110100
110101001 => 111010100 => 011011010
110101010 => 011010101 => 011011001
110101011 => 111010101 => 101101101
110101100 => 011010110 => 011011100
110101101 => 111010110 => 101101110
110101110 => 011010111 => 101100111
110101111 => 111010111 => 110110111
110110000 => 011011000 => 110010100
110110001 => 111011000 => 011101010
110110010 => 011011001 => 011101001
110110011 => 111011001 => 101110101
110110100 => 011011010 => 011101100
110110101 => 111011010 => 101110110
110110110 => 011011011 => 101110011
110110111 => 111011011 => 110111011
110111000 => 011011100 => 011110100
110111001 => 111011100 => 101111010
110111010 => 011011101 => 101111001
110111011 => 111011101 => 110111101
110111100 => 011011110 => 101111100
110111101 => 111011110 => 110111110
110111110 => 011011111 => 110011111
110111111 => 111011111 => 111011111
111000000 => 011100000 => 001010100
111000001 => 111100000 => 010101010
111000010 => 011100001 => 010101001
111000011 => 111100001 => 101010101
111000100 => 011100010 => 010101100
111000101 => 111100010 => 101010110
111000110 => 011100011 => 101010011
111000111 => 111100011 => 110101011
111001000 => 011100100 => 010110100
111001001 => 111100100 => 101011010
111001010 => 011100101 => 101011001
111001011 => 111100101 => 110101101
111001100 => 011100110 => 101011100
111001101 => 111100110 => 110101110
111001110 => 011100111 => 110100111
111001111 => 111100111 => 111010111
111010000 => 011101000 => 011010100
111010001 => 111101000 => 101101010
111010010 => 011101001 => 101101001
111010011 => 111101001 => 110110101
111010100 => 011101010 => 101101100
111010101 => 111101010 => 110110110
111010110 => 011101011 => 110110011
111010111 => 111101011 => 111011011
111011000 => 011101100 => 101110100
111011001 => 111101100 => 110111010
111011010 => 011101101 => 110111001
111011011 => 111101101 => 111011101
111011100 => 011101110 => 110111100
111011101 => 111101110 => 111011110
111011110 => 011101111 => 111001111
111011111 => 111101111 => 111101111
111100000 => 011110000 => 101010100
111100001 => 111110000 => 110101010
111100010 => 011110001 => 110101001
111100011 => 111110001 => 111010101
111100100 => 011110010 => 110101100
111100101 => 111110010 => 111010110
111100110 => 011110011 => 111010011
111100111 => 111110011 => 111101011
111101000 => 011110100 => 110110100
111101001 => 111110100 => 111011010
111101010 => 011110101 => 111011001
111101011 => 111110101 => 111101101
111101100 => 011110110 => 111011100
111101101 => 111110110 => 111101110
111101110 => 011110111 => 111100111
111101111 => 111110111 => 111110111
111110000 => 011111000 => 111010100
111110001 => 111111000 => 111101010
111110010 => 011111001 => 111101001
111110011 => 111111001 => 111110101
111110100 => 011111010 => 111101100
111110101 => 111111010 => 111110110
111110110 => 011111011 => 111110011
111110111 => 111111011 => 111111011
111111000 => 011111100 => 111110100
111111001 => 111111100 => 111111010
111111010 => 011111101 => 111111001
111111011 => 111111101 => 111111101
111111100 => 011111110 => 111111100
111111101 => 111111110 => 111111110
111111110 => 011111111 => 011111111
111111111 => 111111111 => 111111111
1110100010 => 0111010001 => 0110101001
1111000010 => 0111100001 => 1010101001
1111111110 => 0111111111 => 0111111111
1111111101 => 1111111110 => 1111111110
1111110110 => 0111111011 => 1111110011
1111100010 => 0111110001 => 1110101001
1111010010 => 0111101001 => 1101101001
1101000010 => 0110100001 => 0100101001
1011111101 => 1101111110 => 1011111110
1000000010 => 0100000001 => 0000001001
10000000010 => 01000000001 => 00000001001
11111111110 => 01111111111 => 01111111111
0111111101 => 1011111110 => 0111111110
0000000001 => 1000000000 => 0000000010
01111111101 => 10111111110 => 01111111110
00000000001 => 10000000000 => 00000000010
0001011101 => 1000101110 => 1000011110
0000111101 => 1000011110 => 0000111110
0100000010 => 0010000001 => 0000010001
0000000010 => 0000000001 => 0000000001
00000000010 => 00000000001 => 00000000001
0000000101 => 1000000010 => 0000000110
0000001101 => 1000000110 => 0000001110
0000011101 => 1000001110 => 0000011110
0001111101 => 1000111110 => 0001111110
0011111101 => 1001111110 => 0011111110
0000001001 => 1000000100 => 1000000010
00000001101 => 10000000110 => 00000001110
0000010101 => 1000001010 => 1000000110
0000101101 => 1000010110 => 1000001110
0010111101 => 1001011110 => 1000111110
0101111101 => 1010111110 => 1001111110
11111111101 => 11111111110 => 11111111110
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.