Identifier
Mp00096:
Binary words
—Foata bijection⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Images
=>
0=>0=>0=>1=>1
1=>1=>1=>0=>0
00=>00=>00=>11=>11
01=>01=>10=>01=>10
10=>10=>01=>10=>01
11=>11=>11=>00=>00
000=>000=>000=>111=>111
001=>001=>100=>011=>110
010=>100=>001=>110=>101
011=>011=>110=>001=>010
100=>010=>010=>101=>011
101=>101=>101=>010=>100
110=>110=>011=>100=>001
111=>111=>111=>000=>000
0000=>0000=>0000=>1111=>1111
0001=>0001=>1000=>0111=>1110
0010=>1000=>0001=>1110=>1101
0011=>0011=>1100=>0011=>0110
0100=>0100=>0010=>1101=>1011
0101=>1001=>1001=>0110=>1100
0110=>1010=>0101=>1010=>0101
0111=>0111=>1110=>0001=>0010
1000=>0010=>0100=>1011=>0111
1001=>0101=>1010=>0101=>1010
1010=>1100=>0011=>1100=>1001
1011=>1011=>1101=>0010=>0100
1100=>0110=>0110=>1001=>0011
1101=>1101=>1011=>0100=>1000
1110=>1110=>0111=>1000=>0001
1111=>1111=>1111=>0000=>0000
00000=>00000=>00000=>11111=>11111
00001=>00001=>10000=>01111=>11110
00010=>10000=>00001=>11110=>11101
00011=>00011=>11000=>00111=>01110
00100=>01000=>00010=>11101=>11011
00101=>10001=>10001=>01110=>11100
00110=>10010=>01001=>10110=>01101
00111=>00111=>11100=>00011=>00110
01000=>00100=>00100=>11011=>10111
01001=>01001=>10010=>01101=>11010
01010=>11000=>00011=>11100=>11001
01011=>10011=>11001=>00110=>01100
01100=>01010=>01010=>10101=>01011
01101=>10101=>10101=>01010=>10100
01110=>10110=>01101=>10010=>00101
01111=>01111=>11110=>00001=>00010
10000=>00010=>01000=>10111=>01111
10001=>00101=>10100=>01011=>10110
10010=>10100=>00101=>11010=>10101
10011=>01011=>11010=>00101=>01010
10100=>01100=>00110=>11001=>10011
10101=>11001=>10011=>01100=>11000
10110=>11010=>01011=>10100=>01001
10111=>10111=>11101=>00010=>00100
11000=>00110=>01100=>10011=>00111
11001=>01101=>10110=>01001=>10010
11010=>11100=>00111=>11000=>10001
11011=>11011=>11011=>00100=>01000
11100=>01110=>01110=>10001=>00011
11101=>11101=>10111=>01000=>10000
11110=>11110=>01111=>10000=>00001
11111=>11111=>11111=>00000=>00000
000000=>000000=>000000=>111111=>111111
000001=>000001=>100000=>011111=>111110
000010=>100000=>000001=>111110=>111101
000011=>000011=>110000=>001111=>011110
000100=>010000=>000010=>111101=>111011
000101=>100001=>100001=>011110=>111100
000110=>100010=>010001=>101110=>011101
000111=>000111=>111000=>000111=>001110
001000=>001000=>000100=>111011=>110111
001001=>010001=>100010=>011101=>111010
001010=>110000=>000011=>111100=>111001
001011=>100011=>110001=>001110=>011100
001100=>010010=>010010=>101101=>011011
001101=>100101=>101001=>010110=>101100
001110=>100110=>011001=>100110=>001101
001111=>001111=>111100=>000011=>000110
010000=>000100=>001000=>110111=>101111
010001=>001001=>100100=>011011=>110110
010010=>101000=>000101=>111010=>110101
010011=>010011=>110010=>001101=>011010
010100=>011000=>000110=>111001=>110011
010101=>110001=>100011=>011100=>111000
010110=>110010=>010011=>101100=>011001
010111=>100111=>111001=>000110=>001100
011000=>001010=>010100=>101011=>010111
011001=>010101=>101010=>010101=>101010
011010=>110100=>001011=>110100=>101001
011011=>101011=>110101=>001010=>010100
011100=>010110=>011010=>100101=>001011
011101=>101101=>101101=>010010=>100100
011110=>101110=>011101=>100010=>000101
011111=>011111=>111110=>000001=>000010
100000=>000010=>010000=>101111=>011111
100001=>000101=>101000=>010111=>101110
100010=>100100=>001001=>110110=>101101
100011=>001011=>110100=>001011=>010110
100100=>010100=>001010=>110101=>101011
100101=>101001=>100101=>011010=>110100
100110=>101010=>010101=>101010=>010101
100111=>010111=>111010=>000101=>001010
101000=>001100=>001100=>110011=>100111
101001=>011001=>100110=>011001=>110010
101010=>111000=>000111=>111000=>110001
101011=>110011=>110011=>001100=>011000
101100=>011010=>010110=>101001=>010011
101101=>110101=>101011=>010100=>101000
101110=>110110=>011011=>100100=>001001
101111=>101111=>111101=>000010=>000100
110000=>000110=>011000=>100111=>001111
110001=>001101=>101100=>010011=>100110
110010=>101100=>001101=>110010=>100101
110011=>011011=>110110=>001001=>010010
110100=>011100=>001110=>110001=>100011
110101=>111001=>100111=>011000=>110000
110110=>111010=>010111=>101000=>010001
110111=>110111=>111011=>000100=>001000
111000=>001110=>011100=>100011=>000111
111001=>011101=>101110=>010001=>100010
111010=>111100=>001111=>110000=>100001
111011=>111011=>110111=>001000=>010000
111100=>011110=>011110=>100001=>000011
111101=>111101=>101111=>010000=>100000
111110=>111110=>011111=>100000=>000001
111111=>111111=>111111=>000000=>000000
0000000=>0000000=>0000000=>1111111=>1111111
0000001=>0000001=>1000000=>0111111=>1111110
0000010=>1000000=>0000001=>1111110=>1111101
0000011=>0000011=>1100000=>0011111=>0111110
0000100=>0100000=>0000010=>1111101=>1111011
0000101=>1000001=>1000001=>0111110=>1111100
0000110=>1000010=>0100001=>1011110=>0111101
0000111=>0000111=>1110000=>0001111=>0011110
0001000=>0010000=>0000100=>1111011=>1110111
0001001=>0100001=>1000010=>0111101=>1111010
0001010=>1100000=>0000011=>1111100=>1111001
0001011=>1000011=>1100001=>0011110=>0111100
0001100=>0100010=>0100010=>1011101=>0111011
0001101=>1000101=>1010001=>0101110=>1011100
0001110=>1000110=>0110001=>1001110=>0011101
0001111=>0001111=>1111000=>0000111=>0001110
0010000=>0001000=>0001000=>1110111=>1101111
0010001=>0010001=>1000100=>0111011=>1110110
0010010=>1010000=>0000101=>1111010=>1110101
0010011=>0100011=>1100010=>0011101=>0111010
0010100=>0110000=>0000110=>1111001=>1110011
0010101=>1100001=>1000011=>0111100=>1111000
0010110=>1100010=>0100011=>1011100=>0111001
0010111=>1000111=>1110001=>0001110=>0011100
0011000=>0010010=>0100100=>1011011=>0110111
0011001=>0100101=>1010010=>0101101=>1011010
0011010=>1100100=>0010011=>1101100=>1011001
0011011=>1001011=>1101001=>0010110=>0101100
0011100=>0100110=>0110010=>1001101=>0011011
0011101=>1001101=>1011001=>0100110=>1001100
0011110=>1001110=>0111001=>1000110=>0001101
0011111=>0011111=>1111100=>0000011=>0000110
0100000=>0000100=>0010000=>1101111=>1011111
0100001=>0001001=>1001000=>0110111=>1101110
0100010=>1001000=>0001001=>1110110=>1101101
0100011=>0010011=>1100100=>0011011=>0110110
0100100=>0101000=>0001010=>1110101=>1101011
0100101=>1010001=>1000101=>0111010=>1110100
0100110=>1010010=>0100101=>1011010=>0110101
0100111=>0100111=>1110010=>0001101=>0011010
0101000=>0011000=>0001100=>1110011=>1100111
0101001=>0110001=>1000110=>0111001=>1110010
0101010=>1110000=>0000111=>1111000=>1110001
0101011=>1100011=>1100011=>0011100=>0111000
0101100=>0110010=>0100110=>1011001=>0110011
0101101=>1100101=>1010011=>0101100=>1011000
0101110=>1100110=>0110011=>1001100=>0011001
0101111=>1001111=>1111001=>0000110=>0001100
0110000=>0001010=>0101000=>1010111=>0101111
0110001=>0010101=>1010100=>0101011=>1010110
0110010=>1010100=>0010101=>1101010=>1010101
0110011=>0101011=>1101010=>0010101=>0101010
0110100=>0110100=>0010110=>1101001=>1010011
0110101=>1101001=>1001011=>0110100=>1101000
0110110=>1101010=>0101011=>1010100=>0101001
0110111=>1010111=>1110101=>0001010=>0010100
0111000=>0010110=>0110100=>1001011=>0010111
0111001=>0101101=>1011010=>0100101=>1001010
0111010=>1101100=>0011011=>1100100=>1001001
0111011=>1011011=>1101101=>0010010=>0100100
0111100=>0101110=>0111010=>1000101=>0001011
0111101=>1011101=>1011101=>0100010=>1000100
0111110=>1011110=>0111101=>1000010=>0000101
0111111=>0111111=>1111110=>0000001=>0000010
1000000=>0000010=>0100000=>1011111=>0111111
1000001=>0000101=>1010000=>0101111=>1011110
1000010=>1000100=>0010001=>1101110=>1011101
1000011=>0001011=>1101000=>0010111=>0101110
1000100=>0100100=>0010010=>1101101=>1011011
1000101=>1001001=>1001001=>0110110=>1101100
1000110=>1001010=>0101001=>1010110=>0101101
1000111=>0010111=>1110100=>0001011=>0010110
1001000=>0010100=>0010100=>1101011=>1010111
1001001=>0101001=>1001010=>0110101=>1101010
1001010=>1101000=>0001011=>1110100=>1101001
1001011=>1010011=>1100101=>0011010=>0110100
1001100=>0101010=>0101010=>1010101=>0101011
1001101=>1010101=>1010101=>0101010=>1010100
1001110=>1010110=>0110101=>1001010=>0010101
1001111=>0101111=>1111010=>0000101=>0001010
1010000=>0001100=>0011000=>1100111=>1001111
1010001=>0011001=>1001100=>0110011=>1100110
1010010=>1011000=>0001101=>1110010=>1100101
1010011=>0110011=>1100110=>0011001=>0110010
1010100=>0111000=>0001110=>1110001=>1100011
1010101=>1110001=>1000111=>0111000=>1110000
1010110=>1110010=>0100111=>1011000=>0110001
1010111=>1100111=>1110011=>0001100=>0011000
1011000=>0011010=>0101100=>1010011=>0100111
1011001=>0110101=>1010110=>0101001=>1010010
1011010=>1110100=>0010111=>1101000=>1010001
1011011=>1101011=>1101011=>0010100=>0101000
1011100=>0110110=>0110110=>1001001=>0010011
1011101=>1101101=>1011011=>0100100=>1001000
1011110=>1101110=>0111011=>1000100=>0001001
1011111=>1011111=>1111101=>0000010=>0000100
1100000=>0000110=>0110000=>1001111=>0011111
1100001=>0001101=>1011000=>0100111=>1001110
1100010=>1001100=>0011001=>1100110=>1001101
1100011=>0011011=>1101100=>0010011=>0100110
1100100=>0101100=>0011010=>1100101=>1001011
1100101=>1011001=>1001101=>0110010=>1100100
1100110=>1011010=>0101101=>1010010=>0100101
1100111=>0110111=>1110110=>0001001=>0010010
1101000=>0011100=>0011100=>1100011=>1000111
1101001=>0111001=>1001110=>0110001=>1100010
1101010=>1111000=>0001111=>1110000=>1100001
1101011=>1110011=>1100111=>0011000=>0110000
1101100=>0111010=>0101110=>1010001=>0100011
1101101=>1110101=>1010111=>0101000=>1010000
1101110=>1110110=>0110111=>1001000=>0010001
1101111=>1101111=>1111011=>0000100=>0001000
1110000=>0001110=>0111000=>1000111=>0001111
1110001=>0011101=>1011100=>0100011=>1000110
1110010=>1011100=>0011101=>1100010=>1000101
1110011=>0111011=>1101110=>0010001=>0100010
1110100=>0111100=>0011110=>1100001=>1000011
1110101=>1111001=>1001111=>0110000=>1100000
1110110=>1111010=>0101111=>1010000=>0100001
1110111=>1110111=>1110111=>0001000=>0010000
1111000=>0011110=>0111100=>1000011=>0000111
1111001=>0111101=>1011110=>0100001=>1000010
1111010=>1111100=>0011111=>1100000=>1000001
1111011=>1111011=>1101111=>0010000=>0100000
1111100=>0111110=>0111110=>1000001=>0000011
1111101=>1111101=>1011111=>0100000=>1000000
1111110=>1111110=>0111111=>1000000=>0000001
1111111=>1111111=>1111111=>0000000=>0000000
00000000=>00000000=>00000000=>11111111=>11111111
00000001=>00000001=>10000000=>01111111=>11111110
00000010=>10000000=>00000001=>11111110=>11111101
00000011=>00000011=>11000000=>00111111=>01111110
00000100=>01000000=>00000010=>11111101=>11111011
00000101=>10000001=>10000001=>01111110=>11111100
00000110=>10000010=>01000001=>10111110=>01111101
00000111=>00000111=>11100000=>00011111=>00111110
00001000=>00100000=>00000100=>11111011=>11110111
00001001=>01000001=>10000010=>01111101=>11111010
00001010=>11000000=>00000011=>11111100=>11111001
00001011=>10000011=>11000001=>00111110=>01111100
00001100=>01000010=>01000010=>10111101=>01111011
00001101=>10000101=>10100001=>01011110=>10111100
00001110=>10000110=>01100001=>10011110=>00111101
00001111=>00001111=>11110000=>00001111=>00011110
00010000=>00010000=>00001000=>11110111=>11101111
00010001=>00100001=>10000100=>01111011=>11110110
00010010=>10100000=>00000101=>11111010=>11110101
00010011=>01000011=>11000010=>00111101=>01111010
00010100=>01100000=>00000110=>11111001=>11110011
00010101=>11000001=>10000011=>01111100=>11111000
00010110=>11000010=>01000011=>10111100=>01111001
00010111=>10000111=>11100001=>00011110=>00111100
00011000=>00100010=>01000100=>10111011=>01110111
00011001=>01000101=>10100010=>01011101=>10111010
00011010=>11000100=>00100011=>11011100=>10111001
00011011=>10001011=>11010001=>00101110=>01011100
00011100=>01000110=>01100010=>10011101=>00111011
00011101=>10001101=>10110001=>01001110=>10011100
00011110=>10001110=>01110001=>10001110=>00011101
00011111=>00011111=>11111000=>00000111=>00001110
00100000=>00001000=>00010000=>11101111=>11011111
00100001=>00010001=>10001000=>01110111=>11101110
00100010=>10010000=>00001001=>11110110=>11101101
00100011=>00100011=>11000100=>00111011=>01110110
00100100=>01010000=>00001010=>11110101=>11101011
00100101=>10100001=>10000101=>01111010=>11110100
00100110=>10100010=>01000101=>10111010=>01110101
00100111=>01000111=>11100010=>00011101=>00111010
00101000=>00110000=>00001100=>11110011=>11100111
00101001=>01100001=>10000110=>01111001=>11110010
00101010=>11100000=>00000111=>11111000=>11110001
00101011=>11000011=>11000011=>00111100=>01111000
00101100=>01100010=>01000110=>10111001=>01110011
00101101=>11000101=>10100011=>01011100=>10111000
00101110=>11000110=>01100011=>10011100=>00111001
00101111=>10001111=>11110001=>00001110=>00011100
00110000=>00010010=>01001000=>10110111=>01101111
00110001=>00100101=>10100100=>01011011=>10110110
00110010=>10100100=>00100101=>11011010=>10110101
00110011=>01001011=>11010010=>00101101=>01011010
00110100=>01100100=>00100110=>11011001=>10110011
00110101=>11001001=>10010011=>01101100=>11011000
00110110=>11001010=>01010011=>10101100=>01011001
00110111=>10010111=>11101001=>00010110=>00101100
00111000=>00100110=>01100100=>10011011=>00110111
00111001=>01001101=>10110010=>01001101=>10011010
00111010=>11001100=>00110011=>11001100=>10011001
00111011=>10011011=>11011001=>00100110=>01001100
00111100=>01001110=>01110010=>10001101=>00011011
00111101=>10011101=>10111001=>01000110=>10001100
00111110=>10011110=>01111001=>10000110=>00001101
00111111=>00111111=>11111100=>00000011=>00000110
01000000=>00000100=>00100000=>11011111=>10111111
01000001=>00001001=>10010000=>01101111=>11011110
01000010=>10001000=>00010001=>11101110=>11011101
01000011=>00010011=>11001000=>00110111=>01101110
01000100=>01001000=>00010010=>11101101=>11011011
01000101=>10010001=>10001001=>01110110=>11101100
01000110=>10010010=>01001001=>10110110=>01101101
01000111=>00100111=>11100100=>00011011=>00110110
01001000=>00101000=>00010100=>11101011=>11010111
01001001=>01010001=>10001010=>01110101=>11101010
01001010=>11010000=>00001011=>11110100=>11101001
01001011=>10100011=>11000101=>00111010=>01110100
01001100=>01010010=>01001010=>10110101=>01101011
01001101=>10100101=>10100101=>01011010=>10110100
01001110=>10100110=>01100101=>10011010=>00110101
01001111=>01001111=>11110010=>00001101=>00011010
01010000=>00011000=>00011000=>11100111=>11001111
01010001=>00110001=>10001100=>01110011=>11100110
01010010=>10110000=>00001101=>11110010=>11100101
01010011=>01100011=>11000110=>00111001=>01110010
01010100=>01110000=>00001110=>11110001=>11100011
01010101=>11100001=>10000111=>01111000=>11110000
01010110=>11100010=>01000111=>10111000=>01110001
01010111=>11000111=>11100011=>00011100=>00111000
01011000=>00110010=>01001100=>10110011=>01100111
01011001=>01100101=>10100110=>01011001=>10110010
01011010=>11100100=>00100111=>11011000=>10110001
01011011=>11001011=>11010011=>00101100=>01011000
01011100=>01100110=>01100110=>10011001=>00110011
01011101=>11001101=>10110011=>01001100=>10011000
01011110=>11001110=>01110011=>10001100=>00011001
01011111=>10011111=>11111001=>00000110=>00001100
01100000=>00001010=>01010000=>10101111=>01011111
01100001=>00010101=>10101000=>01010111=>10101110
01100010=>10010100=>00101001=>11010110=>10101101
01100011=>00101011=>11010100=>00101011=>01010110
01100100=>01010100=>00101010=>11010101=>10101011
01100101=>10101001=>10010101=>01101010=>11010100
01100110=>10101010=>01010101=>10101010=>01010101
01100111=>01010111=>11101010=>00010101=>00101010
01101000=>00110100=>00101100=>11010011=>10100111
01101001=>01101001=>10010110=>01101001=>11010010
01101010=>11101000=>00010111=>11101000=>11010001
01101011=>11010011=>11001011=>00110100=>01101000
01101100=>01101010=>01010110=>10101001=>01010011
01101101=>11010101=>10101011=>01010100=>10101000
01101110=>11010110=>01101011=>10010100=>00101001
01101111=>10101111=>11110101=>00001010=>00010100
01110000=>00010110=>01101000=>10010111=>00101111
01110001=>00101101=>10110100=>01001011=>10010110
01110010=>10101100=>00110101=>11001010=>10010101
01110011=>01011011=>11011010=>00100101=>01001010
01110100=>01101100=>00110110=>11001001=>10010011
01110101=>11011001=>10011011=>01100100=>11001000
01110110=>11011010=>01011011=>10100100=>01001001
01110111=>10110111=>11101101=>00010010=>00100100
01111000=>00101110=>01110100=>10001011=>00010111
01111001=>01011101=>10111010=>01000101=>10001010
01111010=>11011100=>00111011=>11000100=>10001001
01111011=>10111011=>11011101=>00100010=>01000100
01111100=>01011110=>01111010=>10000101=>00001011
01111101=>10111101=>10111101=>01000010=>10000100
01111110=>10111110=>01111101=>10000010=>00000101
01111111=>01111111=>11111110=>00000001=>00000010
10000000=>00000010=>01000000=>10111111=>01111111
10000001=>00000101=>10100000=>01011111=>10111110
10000010=>10000100=>00100001=>11011110=>10111101
10000011=>00001011=>11010000=>00101111=>01011110
10000100=>01000100=>00100010=>11011101=>10111011
10000101=>10001001=>10010001=>01101110=>11011100
10000110=>10001010=>01010001=>10101110=>01011101
10000111=>00010111=>11101000=>00010111=>00101110
10001000=>00100100=>00100100=>11011011=>10110111
10001001=>01001001=>10010010=>01101101=>11011010
10001010=>11001000=>00010011=>11101100=>11011001
10001011=>10010011=>11001001=>00110110=>01101100
10001100=>01001010=>01010010=>10101101=>01011011
10001101=>10010101=>10101001=>01010110=>10101100
10001110=>10010110=>01101001=>10010110=>00101101
10001111=>00101111=>11110100=>00001011=>00010110
10010000=>00010100=>00101000=>11010111=>10101111
10010001=>00101001=>10010100=>01101011=>11010110
10010010=>10101000=>00010101=>11101010=>11010101
10010011=>01010011=>11001010=>00110101=>01101010
10010100=>01101000=>00010110=>11101001=>11010011
10010101=>11010001=>10001011=>01110100=>11101000
10010110=>11010010=>01001011=>10110100=>01101001
10010111=>10100111=>11100101=>00011010=>00110100
10011000=>00101010=>01010100=>10101011=>01010111
10011001=>01010101=>10101010=>01010101=>10101010
10011010=>11010100=>00101011=>11010100=>10101001
10011011=>10101011=>11010101=>00101010=>01010100
10011100=>01010110=>01101010=>10010101=>00101011
10011101=>10101101=>10110101=>01001010=>10010100
10011110=>10101110=>01110101=>10001010=>00010101
10011111=>01011111=>11111010=>00000101=>00001010
10100000=>00001100=>00110000=>11001111=>10011111
10100001=>00011001=>10011000=>01100111=>11001110
10100010=>10011000=>00011001=>11100110=>11001101
10100011=>00110011=>11001100=>00110011=>01100110
10100100=>01011000=>00011010=>11100101=>11001011
10100101=>10110001=>10001101=>01110010=>11100100
10100110=>10110010=>01001101=>10110010=>01100101
10100111=>01100111=>11100110=>00011001=>00110010
10101000=>00111000=>00011100=>11100011=>11000111
10101001=>01110001=>10001110=>01110001=>11100010
10101010=>11110000=>00001111=>11110000=>11100001
10101011=>11100011=>11000111=>00111000=>01110000
10101100=>01110010=>01001110=>10110001=>01100011
10101101=>11100101=>10100111=>01011000=>10110000
10101110=>11100110=>01100111=>10011000=>00110001
10101111=>11001111=>11110011=>00001100=>00011000
10110000=>00011010=>01011000=>10100111=>01001111
10110001=>00110101=>10101100=>01010011=>10100110
10110010=>10110100=>00101101=>11010010=>10100101
10110011=>01101011=>11010110=>00101001=>01010010
10110100=>01110100=>00101110=>11010001=>10100011
10110101=>11101001=>10010111=>01101000=>11010000
10110110=>11101010=>01010111=>10101000=>01010001
10110111=>11010111=>11101011=>00010100=>00101000
10111000=>00110110=>01101100=>10010011=>00100111
10111001=>01101101=>10110110=>01001001=>10010010
10111010=>11101100=>00110111=>11001000=>10010001
10111011=>11011011=>11011011=>00100100=>01001000
10111100=>01101110=>01110110=>10001001=>00010011
10111101=>11011101=>10111011=>01000100=>10001000
10111110=>11011110=>01111011=>10000100=>00001001
10111111=>10111111=>11111101=>00000010=>00000100
11000000=>00000110=>01100000=>10011111=>00111111
11000001=>00001101=>10110000=>01001111=>10011110
11000010=>10001100=>00110001=>11001110=>10011101
11000011=>00011011=>11011000=>00100111=>01001110
11000100=>01001100=>00110010=>11001101=>10011011
11000101=>10011001=>10011001=>01100110=>11001100
11000110=>10011010=>01011001=>10100110=>01001101
11000111=>00110111=>11101100=>00010011=>00100110
11001000=>00101100=>00110100=>11001011=>10010111
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001001110011=>010100011011=>110110001010=>001001110101=>010011101010
001001100111=>010100010111=>111010001010=>000101110101=>001011101010
001001010111=>110100000111=>111000001011=>000111110100=>001111101000
001001001111=>010100001111=>111100001010=>000011110101=>000111101010
001000011111=>000100011111=>111110001000=>000001110111=>000011101110
000111000111=>001000110111=>111011000100=>000100111011=>001001110110
000110001111=>001000101111=>111101000100=>000010111011=>000101110110
000101010111=>111000000111=>111000000111=>000111111000=>001111110000
000100011111=>001000011111=>111110000100=>000001111011=>000011110110
000011110011=>010000111011=>110111000010=>001000111101=>010001111010
000011100111=>010000110111=>111011000010=>000100111101=>001001111010
000011001111=>010000101111=>111101000010=>000010111101=>000101111010
000010101111=>110000001111=>111100000011=>000011111100=>000111111000
000010011111=>010000011111=>111110000010=>000001111101=>000011111010
000000111111=>000000111111=>111111000000=>000000111111=>000001111110
111111111111=>111111111111=>111111111111=>000000000000=>000000000000
111110011111=>011111011111=>111110111110=>000001000001=>000010000010
111001100001=>000101110101=>101011101000=>010100010111=>101000101110
111000000111=>000001110111=>111011100000=>000100011111=>001000111110
111000110001=>001001110101=>101011100100=>010100011011=>101000110110
100111100111=>010101110111=>111011101010=>000100010101=>001000101010
100111100001=>000101011101=>101110101000=>010001010111=>100010101110
100110011001=>010101010101=>101010101010=>010101010101=>101010101010
100110000111=>000101010111=>111010101000=>000101010111=>001010101110
100001111001=>010001011101=>101110100010=>010001011101=>100010111010
100001100111=>010001010111=>111010100010=>000101011101=>001010111010
100001100001=>000100010101=>101010001000=>010101110111=>101011101110
100000011111=>000001011111=>111110100000=>000001011111=>000010111110
100011000111=>001001010111=>111010100100=>000101011011=>001010110110
100011110001=>001001011101=>101110100100=>010001011011=>100010110110
101101100111=>011101010111=>111010101110=>000101010001=>001010100010
101100011001=>010011010101=>101010110010=>010101001101=>101010011010
101100110001=>001011010101=>101010110100=>010101001011=>101010010110
101111011001=>011101110101=>101011101110=>010100010001=>101000100010
101001110001=>001011001101=>101100110100=>010011001011=>100110010110
101010010101=>110111000001=>100000111011=>011111000100=>111110001000
0000000000=>0000000000=>0000000000=>1111111111=>1111111111
0000011110=>1000001110=>0111000001=>1000111110=>0001111101
0001111110=>1000111110=>0111110001=>1000001110=>0000011101
0111111110=>1011111110=>0111111101=>1000000010=>0000000101
000000000000=>000000000000=>000000000000=>111111111111=>111111111111
0101010100=>0111100000=>0000011110=>1111100001=>1111000011
0000010100=>0110000000=>0000000110=>1111111001=>1111110011
0000000010=>1000000000=>0000000001=>1111111110=>1111111101
0000001110=>1000000110=>0110000001=>1001111110=>0011111101
0000111110=>1000011110=>0111100001=>1000011110=>0000111101
0011111110=>1001111110=>0111111001=>1000000110=>0000001101
00000000010=>10000000000=>00000000001=>11111111110=>11111111101
00000001110=>10000000110=>01100000001=>10011111110=>00111111101
00000111110=>10000011110=>01111000001=>10000111110=>00001111101
00011111110=>10001111110=>01111110001=>10000001110=>00000011101
01111111110=>10111111110=>01111111101=>10000000010=>00000000101
0011110000=>0001001110=>0111001000=>1000110111=>0001101111
0110100100=>0101101000=>0001011010=>1110100101=>1101001011
001010110100=>011110000100=>001000011110=>110111100001=>101111000011
001011010100=>011110001000=>000100011110=>111011100001=>110111000011
001011011000=>001110001010=>010100011100=>101011100011=>010111000111
001011100100=>010110001100=>001100011010=>110011100101=>100111001011
001011101000=>001110001100=>001100011100=>110011100011=>100111000111
001100110100=>011010010100=>001010010110=>110101101001=>101011010011
001101010100=>011110010000=>000010011110=>111101100001=>111011000011
001101011000=>001110010010=>010010011100=>101101100011=>011011000111
001101100100=>010110010100=>001010011010=>110101100101=>101011001011
001101101000=>001110010100=>001010011100=>110101100011=>101011000111
001110010100=>011010011000=>000110010110=>111001101001=>110011010011
001110100100=>010110011000=>000110011010=>111001100101=>110011001011
001110101000=>001110011000=>000110011100=>111001100011=>110011000111
010010110100=>011101000100=>001000101110=>110111010001=>101110100011
010011010100=>011101001000=>000100101110=>111011010001=>110110100011
010011100100=>010101001100=>001100101010=>110011010101=>100110101011
010011101000=>001101001100=>001100101100=>110011010011=>100110100111
010100110100=>011011000100=>001000110110=>110111001001=>101110010011
010101010100=>011111000000=>000000111110=>111111000001=>111110000011
010101100100=>010111000100=>001000111010=>110111000101=>101110001011
010101101000=>001111000100=>001000111100=>110111000011=>101110000111
010110010100=>011011001000=>000100110110=>111011001001=>110110010011
010110100100=>010111001000=>000100111010=>111011000101=>110110001011
010110101000=>001111001000=>000100111100=>111011000011=>110110000111
010111000100=>010011001100=>001100110010=>110011001101=>100110011011
011000110100=>011001010100=>001010100110=>110101011001=>101010110011
011001010100=>011101010000=>000010101110=>111101010001=>111010100011
011001100100=>010101010100=>001010101010=>110101010101=>101010101011
011001101000=>001101010100=>001010101100=>110101010011=>101010100111
011010010100=>011011010000=>000010110110=>111101001001=>111010010011
011010100100=>010111010000=>000010111010=>111101000101=>111010001011
011010101000=>001111010000=>000010111100=>111101000011=>111010000111
011011000100=>010011010100=>001010110010=>110101001101=>101010011011
011100010100=>011001011000=>000110100110=>111001011001=>110010110011
011100100100=>010101011000=>000110101010=>111001010101=>110010101011
011100101000=>001101011000=>000110101100=>111001010011=>110010100111
011101000100=>010011011000=>000110110010=>111001001101=>110010011011
0110010101=>1101010001=>1000101011=>0111010100=>1110101000
0110011001=>0101010101=>1010101010=>0101010101=>1010101010
0110110001=>0011010101=>1010101100=>0101010011=>1010100110
011010010101=>110110100001=>100001011011=>011110100100=>111101001000
011010101001=>011110100001=>100001011110=>011110100001=>111101000010
011011010100=>011110101000=>000101011110=>111010100001=>110101000011
011100011001=>010010110101=>101011010010=>010100101101=>101001011010
011101001100=>010110110010=>010011011010=>101100100101=>011001001011
011101100001=>000110110101=>101011011000=>010100100111=>101001001110
011101110000=>000110110110=>011011011000=>100100100111=>001001001111
0100000100=>0100001000=>0001000010=>1110111101=>1101111011
000111011100=>011000110110=>011011000110=>100100111001=>001001110011
0000000101=>1000000001=>1000000001=>0111111110=>1111111100
0000001101=>1000000101=>1010000001=>0101111110=>1011111100
101110100001=>000111011001=>100110111000=>011001000111=>110010001110
0110111001=>0110101101=>1011010110=>0100101001=>1001010010
0001101001=>0110001001=>1001000110=>0110111001=>1101110010
0000010001=>0010000001=>1000000100=>0111111011=>1111110110
101000111001=>010011001101=>101100110010=>010011001101=>100110011010
100100111001=>010101001101=>101100101010=>010011010101=>100110101010
101001100011=>001011001011=>110100110100=>001011001011=>010110010110
101000110011=>010011001011=>110100110010=>001011001101=>010110011010
100100110011=>010101001011=>110100101010=>001011010101=>010110101010
101010000111=>000111000111=>111000111000=>000111000111=>001110001110
101000100111=>010011000111=>111000110010=>000111001101=>001110011010
110101010101=>111111000001=>100000111111=>011111000000=>111110000000
110110010101=>110111010001=>100010111011=>011101000100=>111010001000
111001010101=>111011100001=>100001110111=>011110001000=>111100010000
111010010101=>110111100001=>100001111011=>011110000100=>111100001000
111100010101=>110011110001=>100011110011=>011100001100=>111000011000
111100100101=>101011110001=>100011110101=>011100001010=>111000010100
0110010011=>0101010011=>1100101010=>0011010101=>0110101010
101100010011=>010011010011=>110010110010=>001101001101=>011010011010
011100000111=>000010110111=>111011010000=>000100101111=>001001011110
0101000000=>0000011000=>0001100000=>1110011111=>1100111111
110011010101=>111011010001=>100010110111=>011101001000=>111010010000
110100110101=>110111001001=>100100111011=>011011000100=>110110001000
110001110101=>110011011001=>100110110011=>011001001100=>110010011000
110011001101=>101011010101=>101010110101=>010101001010=>101010010100
100110011011=>101010101011=>110101010101=>001010101010=>010101010100
0000000011=>0000000011=>1100000000=>0011111111=>0111111110
0011111111=>0011111111=>1111111100=>0000000011=>0000000110
00000000011=>00000000011=>11000000000=>00111111111=>01111111110
00111111111=>00111111111=>11111111100=>00000000011=>00000000110
0011111100=>0100111110=>0111110010=>1000001101=>0000011011
0110100111=>0110100111=>1110010110=>0001101001=>0011010010
0100101001=>0110100001=>1000010110=>0111101001=>1111010010
011000100001=>000100101001=>100101001000=>011010110111=>110101101110
010010100001=>000110100001=>100001011000=>011110100111=>111101001110
010000101001=>011000100001=>100001000110=>011110111001=>111101110010
101101000011=>000111010011=>110010111000=>001101000111=>011010001110
0011010111=>1100100111=>1110010011=>0001101100=>0011011000
0011110101=>1100111001=>1001110011=>0110001100=>1100011000
0000011011=>1000001011=>1101000001=>0010111110=>0101111100
111000110101=>110011101001=>100101110011=>011010001100=>110100011000
0011011111=>1001011111=>1111101001=>0000010110=>0000101100
011110100101=>101101110001=>100011101101=>011100010010=>111000100100
0100111001=>0101001101=>1011001010=>0100110101=>1001101010
010011011001=>011010010101=>101010010110=>010101101001=>101011010010
0101100001=>0001100101=>1010011000=>0101100111=>1011001110
100100100001=>000101010001=>100010101000=>011101010111=>111010101110
0101111001=>0110011101=>1011100110=>0100011001=>1000110010
0110100011=>0011010011=>1100101100=>0011010011=>0110100110
0001010000=>0001100000=>0000011000=>1111100111=>1111001111
0001000100=>0100100000=>0000010010=>1111101101=>1111011011
010100000000=>000000011000=>000110000000=>111001111111=>110011111111
000101000000=>000001100000=>000001100000=>111110011111=>111100111111
010001000000=>000001001000=>000100100000=>111011011111=>110110111111
000001010000=>000110000000=>000000011000=>111111100111=>111111001111
010101010000=>000111100000=>000001111000=>111110000111=>111100001111
000100010000=>000100100000=>000001001000=>111110110111=>111101101111
011010010000=>000101101000=>000101101000=>111010010111=>110100101111
000000010100=>011000000000=>000000000110=>111111111001=>111111110011
010100010100=>011001100000=>000001100110=>111110011001=>111100110011
000101010100=>011110000000=>000000011110=>111111100001=>111111000011
000100000100=>010000100000=>000001000010=>111110111101=>111101111011
011010000100=>010001101000=>000101100010=>111010011101=>110100111011
000110100100=>010110001000=>000100011010=>111011100101=>110111001011
011000100100=>010100101000=>000101001010=>111010110101=>110101101011
0011011110=>1100101110=>0111010011=>1000101100=>0001011001
0011101110=>1100110110=>0110110011=>1001001100=>0010011001
0011110110=>1100111010=>0101110011=>1010001100=>0100011001
011101010101=>111101100001=>100001101111=>011110010000=>111100100000
011100110101=>110101101001=>100101101011=>011010010100=>110100101000
001111010101=>111001110001=>100011100111=>011100011000=>111000110000
011110010101=>110101110001=>100011101011=>011100010100=>111000101000
Map
Foata bijection
Description
The Foata bijection $\phi$ is a bijection on the set of words of given content (by a slight generalization of Section 2 in [1]).
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
For instance, to compute $\phi(4154223)$, the sequence of words is
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
For instance, to compute $\phi(4154223)$, the sequence of words is
- 4,
- |4|1 -- > 41,
- |4|1|5 -- > 415,
- |415|4 -- > 5414,
- |5|4|14|2 -- > 54412,
- |5441|2|2 -- > 154422,
- |1|5442|2|3 -- > 1254423.
Map
reverse
Description
Return the reversal of a binary word.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
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.
This is the word obtained by moving the first letter to the end.
searching the database
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