Identifier
Mp00105:
Binary words
—complement⟶
Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
0=>1=>1=>1
1=>0=>0=>0
00=>11=>11=>11
01=>10=>10=>01
10=>01=>01=>10
11=>00=>00=>00
000=>111=>111=>111
001=>110=>110=>011
010=>101=>101=>101
011=>100=>010=>010
100=>011=>011=>110
101=>010=>100=>001
110=>001=>001=>100
111=>000=>000=>000
0000=>1111=>1111=>1111
0001=>1110=>1110=>0111
0010=>1101=>1101=>1011
0011=>1100=>0110=>0110
0100=>1011=>1011=>1101
0101=>1010=>1100=>0011
0110=>1001=>0101=>1010
0111=>1000=>0010=>0100
1000=>0111=>0111=>1110
1001=>0110=>1010=>0101
1010=>0101=>1001=>1001
1011=>0100=>0100=>0010
1100=>0011=>0011=>1100
1101=>0010=>1000=>0001
1110=>0001=>0001=>1000
1111=>0000=>0000=>0000
00000=>11111=>11111=>11111
00001=>11110=>11110=>01111
00010=>11101=>11101=>10111
00011=>11100=>01110=>01110
00100=>11011=>11011=>11011
00101=>11010=>11100=>00111
00110=>11001=>01101=>10110
00111=>11000=>00110=>01100
01000=>10111=>10111=>11101
01001=>10110=>11010=>01011
01010=>10101=>11001=>10011
01011=>10100=>01100=>00110
01100=>10011=>01011=>11010
01101=>10010=>10100=>00101
01110=>10001=>00101=>10100
01111=>10000=>00010=>01000
10000=>01111=>01111=>11110
10001=>01110=>10110=>01101
10010=>01101=>10101=>10101
10011=>01100=>01010=>01010
10100=>01011=>10011=>11001
10101=>01010=>11000=>00011
10110=>01001=>01001=>10010
10111=>01000=>00100=>00100
11000=>00111=>00111=>11100
11001=>00110=>10010=>01001
11010=>00101=>10001=>10001
11011=>00100=>01000=>00010
11100=>00011=>00011=>11000
11101=>00010=>10000=>00001
11110=>00001=>00001=>10000
11111=>00000=>00000=>00000
000000=>111111=>111111=>111111
000001=>111110=>111110=>011111
000010=>111101=>111101=>101111
000011=>111100=>011110=>011110
000100=>111011=>111011=>110111
000101=>111010=>111100=>001111
000110=>111001=>011101=>101110
000111=>111000=>001110=>011100
001000=>110111=>110111=>111011
001001=>110110=>111010=>010111
001010=>110101=>111001=>100111
001011=>110100=>011100=>001110
001100=>110011=>011011=>110110
001101=>110010=>101100=>001101
001110=>110001=>001101=>101100
001111=>110000=>000110=>011000
010000=>101111=>101111=>111101
010001=>101110=>110110=>011011
010010=>101101=>110101=>101011
010011=>101100=>011010=>010110
010100=>101011=>110011=>110011
010101=>101010=>111000=>000111
010110=>101001=>011001=>100110
010111=>101000=>001100=>001100
011000=>100111=>010111=>111010
011001=>100110=>101010=>010101
011010=>100101=>101001=>100101
011011=>100100=>010100=>001010
011100=>100011=>001011=>110100
011101=>100010=>100100=>001001
011110=>100001=>000101=>101000
011111=>100000=>000010=>010000
100000=>011111=>011111=>111110
100001=>011110=>101110=>011101
100010=>011101=>101101=>101101
100011=>011100=>010110=>011010
100100=>011011=>101011=>110101
100101=>011010=>110100=>001011
100110=>011001=>010101=>101010
100111=>011000=>001010=>010100
101000=>010111=>100111=>111001
101001=>010110=>110010=>010011
101010=>010101=>110001=>100011
101011=>010100=>011000=>000110
101100=>010011=>010011=>110010
101101=>010010=>101000=>000101
101110=>010001=>001001=>100100
101111=>010000=>000100=>001000
110000=>001111=>001111=>111100
110001=>001110=>100110=>011001
110010=>001101=>100101=>101001
110011=>001100=>010010=>010010
110100=>001011=>100011=>110001
110101=>001010=>110000=>000011
110110=>001001=>010001=>100010
110111=>001000=>001000=>000100
111000=>000111=>000111=>111000
111001=>000110=>100010=>010001
111010=>000101=>100001=>100001
111011=>000100=>010000=>000010
111100=>000011=>000011=>110000
111101=>000010=>100000=>000001
111110=>000001=>000001=>100000
111111=>000000=>000000=>000000
0000000=>1111111=>1111111=>1111111
0000001=>1111110=>1111110=>0111111
0000010=>1111101=>1111101=>1011111
0000011=>1111100=>0111110=>0111110
0000100=>1111011=>1111011=>1101111
0000101=>1111010=>1111100=>0011111
0000110=>1111001=>0111101=>1011110
0000111=>1111000=>0011110=>0111100
0001000=>1110111=>1110111=>1110111
0001001=>1110110=>1111010=>0101111
0001010=>1110101=>1111001=>1001111
0001011=>1110100=>0111100=>0011110
0001100=>1110011=>0111011=>1101110
0001101=>1110010=>1011100=>0011101
0001110=>1110001=>0011101=>1011100
0001111=>1110000=>0001110=>0111000
0010000=>1101111=>1101111=>1111011
0010001=>1101110=>1110110=>0110111
0010010=>1101101=>1110101=>1010111
0010011=>1101100=>0111010=>0101110
0010100=>1101011=>1110011=>1100111
0010101=>1101010=>1111000=>0001111
0010110=>1101001=>0111001=>1001110
0010111=>1101000=>0011100=>0011100
0011000=>1100111=>0110111=>1110110
0011001=>1100110=>1011010=>0101101
0011010=>1100101=>1011001=>1001101
0011011=>1100100=>0101100=>0011010
0011100=>1100011=>0011011=>1101100
0011101=>1100010=>1001100=>0011001
0011110=>1100001=>0001101=>1011000
0011111=>1100000=>0000110=>0110000
0100000=>1011111=>1011111=>1111101
0100001=>1011110=>1101110=>0111011
0100010=>1011101=>1101101=>1011011
0100011=>1011100=>0110110=>0110110
0100100=>1011011=>1101011=>1101011
0100101=>1011010=>1110100=>0010111
0100110=>1011001=>0110101=>1010110
0100111=>1011000=>0011010=>0101100
0101000=>1010111=>1100111=>1110011
0101001=>1010110=>1110010=>0100111
0101010=>1010101=>1110001=>1000111
0101011=>1010100=>0111000=>0001110
0101100=>1010011=>0110011=>1100110
0101101=>1010010=>1011000=>0001101
0101110=>1010001=>0011001=>1001100
0101111=>1010000=>0001100=>0011000
0110000=>1001111=>0101111=>1111010
0110001=>1001110=>1010110=>0110101
0110010=>1001101=>1010101=>1010101
0110011=>1001100=>0101010=>0101010
0110100=>1001011=>1010011=>1100101
0110101=>1001010=>1101000=>0001011
0110110=>1001001=>0101001=>1001010
0110111=>1001000=>0010100=>0010100
0111000=>1000111=>0010111=>1110100
0111001=>1000110=>1001010=>0101001
0111010=>1000101=>1001001=>1001001
0111011=>1000100=>0100100=>0010010
0111100=>1000011=>0001011=>1101000
0111101=>1000010=>1000100=>0010001
0111110=>1000001=>0000101=>1010000
0111111=>1000000=>0000010=>0100000
1000000=>0111111=>0111111=>1111110
1000001=>0111110=>1011110=>0111101
1000010=>0111101=>1011101=>1011101
1000011=>0111100=>0101110=>0111010
1000100=>0111011=>1011011=>1101101
1000101=>0111010=>1101100=>0011011
1000110=>0111001=>0101101=>1011010
1000111=>0111000=>0010110=>0110100
1001000=>0110111=>1010111=>1110101
1001001=>0110110=>1101010=>0101011
1001010=>0110101=>1101001=>1001011
1001011=>0110100=>0110100=>0010110
1001100=>0110011=>0101011=>1101010
1001101=>0110010=>1010100=>0010101
1001110=>0110001=>0010101=>1010100
1001111=>0110000=>0001010=>0101000
1010000=>0101111=>1001111=>1111001
1010001=>0101110=>1100110=>0110011
1010010=>0101101=>1100101=>1010011
1010011=>0101100=>0110010=>0100110
1010100=>0101011=>1100011=>1100011
1010101=>0101010=>1110000=>0000111
1010110=>0101001=>0110001=>1000110
1010111=>0101000=>0011000=>0001100
1011000=>0100111=>0100111=>1110010
1011001=>0100110=>1010010=>0100101
1011010=>0100101=>1010001=>1000101
1011011=>0100100=>0101000=>0001010
1011100=>0100011=>0010011=>1100100
1011101=>0100010=>1001000=>0001001
1011110=>0100001=>0001001=>1001000
1011111=>0100000=>0000100=>0010000
1100000=>0011111=>0011111=>1111100
1100001=>0011110=>1001110=>0111001
1100010=>0011101=>1001101=>1011001
1100011=>0011100=>0100110=>0110010
1100100=>0011011=>1001011=>1101001
1100101=>0011010=>1100100=>0010011
1100110=>0011001=>0100101=>1010010
1100111=>0011000=>0010010=>0100100
1101000=>0010111=>1000111=>1110001
1101001=>0010110=>1100010=>0100011
1101010=>0010101=>1100001=>1000011
1101011=>0010100=>0110000=>0000110
1101100=>0010011=>0100011=>1100010
1101101=>0010010=>1010000=>0000101
1101110=>0010001=>0010001=>1000100
1101111=>0010000=>0001000=>0001000
1110000=>0001111=>0001111=>1111000
1110001=>0001110=>1000110=>0110001
1110010=>0001101=>1000101=>1010001
1110011=>0001100=>0100010=>0100010
1110100=>0001011=>1000011=>1100001
1110101=>0001010=>1100000=>0000011
1110110=>0001001=>0100001=>1000010
1110111=>0001000=>0010000=>0000100
1111000=>0000111=>0000111=>1110000
1111001=>0000110=>1000010=>0100001
1111010=>0000101=>1000001=>1000001
1111011=>0000100=>0100000=>0000010
1111100=>0000011=>0000011=>1100000
1111101=>0000010=>1000000=>0000001
1111110=>0000001=>0000001=>1000000
1111111=>0000000=>0000000=>0000000
00000000=>11111111=>11111111=>11111111
00000001=>11111110=>11111110=>01111111
00000010=>11111101=>11111101=>10111111
00000011=>11111100=>01111110=>01111110
00000100=>11111011=>11111011=>11011111
00000101=>11111010=>11111100=>00111111
00000110=>11111001=>01111101=>10111110
00000111=>11111000=>00111110=>01111100
00001000=>11110111=>11110111=>11101111
00001001=>11110110=>11111010=>01011111
00001010=>11110101=>11111001=>10011111
00001011=>11110100=>01111100=>00111110
00001100=>11110011=>01111011=>11011110
00001101=>11110010=>10111100=>00111101
00001110=>11110001=>00111101=>10111100
00001111=>11110000=>00011110=>01111000
00010000=>11101111=>11101111=>11110111
00010001=>11101110=>11110110=>01101111
00010010=>11101101=>11110101=>10101111
00010011=>11101100=>01111010=>01011110
00010100=>11101011=>11110011=>11001111
00010101=>11101010=>11111000=>00011111
00010110=>11101001=>01111001=>10011110
00010111=>11101000=>00111100=>00111100
00011000=>11100111=>01110111=>11101110
00011001=>11100110=>10111010=>01011101
00011010=>11100101=>10111001=>10011101
00011011=>11100100=>01011100=>00111010
00011100=>11100011=>00111011=>11011100
00011101=>11100010=>10011100=>00111001
00011110=>11100001=>00011101=>10111000
00011111=>11100000=>00001110=>01110000
00100000=>11011111=>11011111=>11111011
00100001=>11011110=>11101110=>01110111
00100010=>11011101=>11101101=>10110111
00100011=>11011100=>01110110=>01101110
00100100=>11011011=>11101011=>11010111
00100101=>11011010=>11110100=>00101111
00100110=>11011001=>01110101=>10101110
00100111=>11011000=>00111010=>01011100
00101000=>11010111=>11100111=>11100111
00101001=>11010110=>11110010=>01001111
00101010=>11010101=>11110001=>10001111
00101011=>11010100=>01111000=>00011110
00101100=>11010011=>01110011=>11001110
00101101=>11010010=>10111000=>00011101
00101110=>11010001=>00111001=>10011100
00101111=>11010000=>00011100=>00111000
00110000=>11001111=>01101111=>11110110
00110001=>11001110=>10110110=>01101101
00110010=>11001101=>10110101=>10101101
00110011=>11001100=>01011010=>01011010
00110100=>11001011=>10110011=>11001101
00110101=>11001010=>11011000=>00011011
00110110=>11001001=>01011001=>10011010
00110111=>11001000=>00101100=>00110100
00111000=>11000111=>00110111=>11101100
00111001=>11000110=>10011010=>01011001
00111010=>11000101=>10011001=>10011001
00111011=>11000100=>01001100=>00110010
00111100=>11000011=>00011011=>11011000
00111101=>11000010=>10001100=>00110001
00111110=>11000001=>00001101=>10110000
00111111=>11000000=>00000110=>01100000
01000000=>10111111=>10111111=>11111101
01000001=>10111110=>11011110=>01111011
01000010=>10111101=>11011101=>10111011
01000011=>10111100=>01101110=>01110110
01000100=>10111011=>11011011=>11011011
01000101=>10111010=>11101100=>00110111
01000110=>10111001=>01101101=>10110110
01000111=>10111000=>00110110=>01101100
01001000=>10110111=>11010111=>11101011
01001001=>10110110=>11101010=>01010111
01001010=>10110101=>11101001=>10010111
01001011=>10110100=>01110100=>00101110
01001100=>10110011=>01101011=>11010110
01001101=>10110010=>10110100=>00101101
01001110=>10110001=>00110101=>10101100
01001111=>10110000=>00011010=>01011000
01010000=>10101111=>11001111=>11110011
01010001=>10101110=>11100110=>01100111
01010010=>10101101=>11100101=>10100111
01010011=>10101100=>01110010=>01001110
01010100=>10101011=>11100011=>11000111
01010101=>10101010=>11110000=>00001111
01010110=>10101001=>01110001=>10001110
01010111=>10101000=>00111000=>00011100
01011000=>10100111=>01100111=>11100110
01011001=>10100110=>10110010=>01001101
01011010=>10100101=>10110001=>10001101
01011011=>10100100=>01011000=>00011010
01011100=>10100011=>00110011=>11001100
01011101=>10100010=>10011000=>00011001
01011110=>10100001=>00011001=>10011000
01011111=>10100000=>00001100=>00110000
01100000=>10011111=>01011111=>11111010
01100001=>10011110=>10101110=>01110101
01100010=>10011101=>10101101=>10110101
01100011=>10011100=>01010110=>01101010
01100100=>10011011=>10101011=>11010101
01100101=>10011010=>11010100=>00101011
01100110=>10011001=>01010101=>10101010
01100111=>10011000=>00101010=>01010100
01101000=>10010111=>10100111=>11100101
01101001=>10010110=>11010010=>01001011
01101010=>10010101=>11010001=>10001011
01101011=>10010100=>01101000=>00010110
01101100=>10010011=>01010011=>11001010
01101101=>10010010=>10101000=>00010101
01101110=>10010001=>00101001=>10010100
01101111=>10010000=>00010100=>00101000
01110000=>10001111=>00101111=>11110100
01110001=>10001110=>10010110=>01101001
01110010=>10001101=>10010101=>10101001
01110011=>10001100=>01001010=>01010010
01110100=>10001011=>10010011=>11001001
01110101=>10001010=>11001000=>00010011
01110110=>10001001=>01001001=>10010010
01110111=>10001000=>00100100=>00100100
01111000=>10000111=>00010111=>11101000
01111001=>10000110=>10001010=>01010001
01111010=>10000101=>10001001=>10010001
01111011=>10000100=>01000100=>00100010
01111100=>10000011=>00001011=>11010000
01111101=>10000010=>10000100=>00100001
01111110=>10000001=>00000101=>10100000
01111111=>10000000=>00000010=>01000000
10000000=>01111111=>01111111=>11111110
10000001=>01111110=>10111110=>01111101
10000010=>01111101=>10111101=>10111101
10000011=>01111100=>01011110=>01111010
10000100=>01111011=>10111011=>11011101
10000101=>01111010=>11011100=>00111011
10000110=>01111001=>01011101=>10111010
10000111=>01111000=>00101110=>01110100
10001000=>01110111=>10110111=>11101101
10001001=>01110110=>11011010=>01011011
10001010=>01110101=>11011001=>10011011
10001011=>01110100=>01101100=>00110110
10001100=>01110011=>01011011=>11011010
10001101=>01110010=>10101100=>00110101
10001110=>01110001=>00101101=>10110100
10001111=>01110000=>00010110=>01101000
10010000=>01101111=>10101111=>11110101
10010001=>01101110=>11010110=>01101011
10010010=>01101101=>11010101=>10101011
10010011=>01101100=>01101010=>01010110
10010100=>01101011=>11010011=>11001011
10010101=>01101010=>11101000=>00010111
10010110=>01101001=>01101001=>10010110
10010111=>01101000=>00110100=>00101100
10011000=>01100111=>01010111=>11101010
10011001=>01100110=>10101010=>01010101
10011010=>01100101=>10101001=>10010101
10011011=>01100100=>01010100=>00101010
10011100=>01100011=>00101011=>11010100
10011101=>01100010=>10010100=>00101001
10011110=>01100001=>00010101=>10101000
10011111=>01100000=>00001010=>01010000
10100000=>01011111=>10011111=>11111001
10100001=>01011110=>11001110=>01110011
10100010=>01011101=>11001101=>10110011
10100011=>01011100=>01100110=>01100110
10100100=>01011011=>11001011=>11010011
10100101=>01011010=>11100100=>00100111
10100110=>01011001=>01100101=>10100110
10100111=>01011000=>00110010=>01001100
10101000=>01010111=>11000111=>11100011
10101001=>01010110=>11100010=>01000111
10101010=>01010101=>11100001=>10000111
10101011=>01010100=>01110000=>00001110
10101100=>01010011=>01100011=>11000110
10101101=>01010010=>10110000=>00001101
10101110=>01010001=>00110001=>10001100
10101111=>01010000=>00011000=>00011000
10110000=>01001111=>01001111=>11110010
10110001=>01001110=>10100110=>01100101
10110010=>01001101=>10100101=>10100101
10110011=>01001100=>01010010=>01001010
10110100=>01001011=>10100011=>11000101
10110101=>01001010=>11010000=>00001011
10110110=>01001001=>01010001=>10001010
10110111=>01001000=>00101000=>00010100
10111000=>01000111=>00100111=>11100100
10111001=>01000110=>10010010=>01001001
10111010=>01000101=>10010001=>10001001
10111011=>01000100=>01001000=>00010010
10111100=>01000011=>00010011=>11001000
10111101=>01000010=>10001000=>00010001
10111110=>01000001=>00001001=>10010000
10111111=>01000000=>00000100=>00100000
11000000=>00111111=>00111111=>11111100
11000001=>00111110=>10011110=>01111001
11000010=>00111101=>10011101=>10111001
11000011=>00111100=>01001110=>01110010
11000100=>00111011=>10011011=>11011001
11000101=>00111010=>11001100=>00110011
11000110=>00111001=>01001101=>10110010
11000111=>00111000=>00100110=>01100100
11001000=>00110111=>10010111=>11101001
11001001=>00110110=>11001010=>01010011
11001010=>00110101=>11001001=>10010011
11001011=>00110100=>01100100=>00100110
11001100=>00110011=>01001011=>11010010
11001101=>00110010=>10100100=>00100101
11001110=>00110001=>00100101=>10100100
11001111=>00110000=>00010010=>01001000
11010000=>00101111=>10001111=>11110001
11010001=>00101110=>11000110=>01100011
11010010=>00101101=>11000101=>10100011
11010011=>00101100=>01100010=>01000110
11010100=>00101011=>11000011=>11000011
11010101=>00101010=>11100000=>00000111
11010110=>00101001=>01100001=>10000110
11010111=>00101000=>00110000=>00001100
11011000=>00100111=>01000111=>11100010
11011001=>00100110=>10100010=>01000101
11011010=>00100101=>10100001=>10000101
11011011=>00100100=>01010000=>00001010
11011100=>00100011=>00100011=>11000100
11011101=>00100010=>10010000=>00001001
11011110=>00100001=>00010001=>10001000
11011111=>00100000=>00001000=>00010000
11100000=>00011111=>00011111=>11111000
11100001=>00011110=>10001110=>01110001
11100010=>00011101=>10001101=>10110001
11100011=>00011100=>01000110=>01100010
11100100=>00011011=>10001011=>11010001
11100101=>00011010=>11000100=>00100011
11100110=>00011001=>01000101=>10100010
11100111=>00011000=>00100010=>01000100
11101000=>00010111=>10000111=>11100001
11101001=>00010110=>11000010=>01000011
11101010=>00010101=>11000001=>10000011
11101011=>00010100=>01100000=>00000110
11101100=>00010011=>01000011=>11000010
11101101=>00010010=>10100000=>00000101
11101110=>00010001=>00100001=>10000100
11101111=>00010000=>00010000=>00001000
11110000=>00001111=>00001111=>11110000
11110001=>00001110=>10000110=>01100001
11110010=>00001101=>10000101=>10100001
11110011=>00001100=>01000010=>01000010
11110100=>00001011=>10000011=>11000001
11110101=>00001010=>11000000=>00000011
11110110=>00001001=>01000001=>10000010
11110111=>00001000=>00100000=>00000100
11111000=>00000111=>00000111=>11100000
11111001=>00000110=>10000010=>01000001
11111010=>00000101=>10000001=>10000001
11111011=>00000100=>01000000=>00000010
11111100=>00000011=>00000011=>11000000
11111101=>00000010=>10000000=>00000001
11111110=>00000001=>00000001=>10000000
11111111=>00000000=>00000000=>00000000
000000000=>111111111=>111111111=>111111111
000000001=>111111110=>111111110=>011111111
000000010=>111111101=>111111101=>101111111
000000011=>111111100=>011111110=>011111110
000000100=>111111011=>111111011=>110111111
000000101=>111111010=>111111100=>001111111
000000110=>111111001=>011111101=>101111110
000000111=>111111000=>001111110=>011111100
000001000=>111110111=>111110111=>111011111
000001001=>111110110=>111111010=>010111111
000001010=>111110101=>111111001=>100111111
000001011=>111110100=>011111100=>001111110
000001100=>111110011=>011111011=>110111110
000001101=>111110010=>101111100=>001111101
000001110=>111110001=>001111101=>101111100
000001111=>111110000=>000111110=>011111000
000010000=>111101111=>111101111=>111101111
000010001=>111101110=>111110110=>011011111
000010010=>111101101=>111110101=>101011111
000010011=>111101100=>011111010=>010111110
000010100=>111101011=>111110011=>110011111
000010101=>111101010=>111111000=>000111111
000010110=>111101001=>011111001=>100111110
000010111=>111101000=>001111100=>001111100
000011000=>111100111=>011110111=>111011110
000011001=>111100110=>101111010=>010111101
000011010=>111100101=>101111001=>100111101
000011011=>111100100=>010111100=>001111010
000011100=>111100011=>001111011=>110111100
000011101=>111100010=>100111100=>001111001
000011110=>111100001=>000111101=>101111000
000011111=>111100000=>000011110=>011110000
000100000=>111011111=>111011111=>111110111
000100001=>111011110=>111101110=>011101111
000100010=>111011101=>111101101=>101101111
000100011=>111011100=>011110110=>011011110
000100100=>111011011=>111101011=>110101111
000100101=>111011010=>111110100=>001011111
000100110=>111011001=>011110101=>101011110
000100111=>111011000=>001111010=>010111100
000101000=>111010111=>111100111=>111001111
000101001=>111010110=>111110010=>010011111
000101010=>111010101=>111110001=>100011111
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11111111100=>00000000011=>00000000011=>11000000000
0011010001=>1100101110=>1101100110=>0110011011
0001000111=>1110111000=>0011110110=>0110111100
0001001101=>1110110010=>1011110100=>0010111101
0001010011=>1110101100=>0111110010=>0100111110
0000101011=>1111010100=>0111111000=>0001111110
0110011101=>1001100010=>1001010100=>0010101001
0111001101=>1000110010=>1010010100=>0010100101
100010111000=>011101000111=>001101100111=>111001101100
0100111101=>1011000010=>1000110100=>0010110001
00111100001=>11000011110=>10001101110=>01110110001
100010101100=>011101010011=>011101100011=>110001101110
100011001010=>011100110101=>110101101001=>100101101011
100011100010=>011100011101=>100101101101=>101101101001
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
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.
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