Identifier
Mp00096:
Binary words
—Foata bijection⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
=>
0=>0=>0=>1
1=>1=>1=>0
00=>00=>00=>11
01=>01=>10=>01
10=>10=>01=>10
11=>11=>11=>00
000=>000=>000=>111
001=>001=>100=>011
010=>100=>001=>110
011=>011=>110=>001
100=>010=>010=>101
101=>101=>101=>010
110=>110=>011=>100
111=>111=>111=>000
0000=>0000=>0000=>1111
0001=>0001=>1000=>0111
0010=>1000=>0001=>1110
0011=>0011=>1100=>0011
0100=>0100=>0010=>1101
0101=>1001=>1001=>0110
0110=>1010=>0101=>1010
0111=>0111=>1110=>0001
1000=>0010=>0100=>1011
1001=>0101=>1010=>0101
1010=>1100=>0011=>1100
1011=>1011=>1101=>0010
1100=>0110=>0110=>1001
1101=>1101=>1011=>0100
1110=>1110=>0111=>1000
1111=>1111=>1111=>0000
00000=>00000=>00000=>11111
00001=>00001=>10000=>01111
00010=>10000=>00001=>11110
00011=>00011=>11000=>00111
00100=>01000=>00010=>11101
00101=>10001=>10001=>01110
00110=>10010=>01001=>10110
00111=>00111=>11100=>00011
01000=>00100=>00100=>11011
01001=>01001=>10010=>01101
01010=>11000=>00011=>11100
01011=>10011=>11001=>00110
01100=>01010=>01010=>10101
01101=>10101=>10101=>01010
01110=>10110=>01101=>10010
01111=>01111=>11110=>00001
10000=>00010=>01000=>10111
10001=>00101=>10100=>01011
10010=>10100=>00101=>11010
10011=>01011=>11010=>00101
10100=>01100=>00110=>11001
10101=>11001=>10011=>01100
10110=>11010=>01011=>10100
10111=>10111=>11101=>00010
11000=>00110=>01100=>10011
11001=>01101=>10110=>01001
11010=>11100=>00111=>11000
11011=>11011=>11011=>00100
11100=>01110=>01110=>10001
11101=>11101=>10111=>01000
11110=>11110=>01111=>10000
11111=>11111=>11111=>00000
000000=>000000=>000000=>111111
000001=>000001=>100000=>011111
000010=>100000=>000001=>111110
000011=>000011=>110000=>001111
000100=>010000=>000010=>111101
000101=>100001=>100001=>011110
000110=>100010=>010001=>101110
000111=>000111=>111000=>000111
001000=>001000=>000100=>111011
001001=>010001=>100010=>011101
001010=>110000=>000011=>111100
001011=>100011=>110001=>001110
001100=>010010=>010010=>101101
001101=>100101=>101001=>010110
001110=>100110=>011001=>100110
001111=>001111=>111100=>000011
010000=>000100=>001000=>110111
010001=>001001=>100100=>011011
010010=>101000=>000101=>111010
010011=>010011=>110010=>001101
010100=>011000=>000110=>111001
010101=>110001=>100011=>011100
010110=>110010=>010011=>101100
010111=>100111=>111001=>000110
011000=>001010=>010100=>101011
011001=>010101=>101010=>010101
011010=>110100=>001011=>110100
011011=>101011=>110101=>001010
011100=>010110=>011010=>100101
011101=>101101=>101101=>010010
011110=>101110=>011101=>100010
011111=>011111=>111110=>000001
100000=>000010=>010000=>101111
100001=>000101=>101000=>010111
100010=>100100=>001001=>110110
100011=>001011=>110100=>001011
100100=>010100=>001010=>110101
100101=>101001=>100101=>011010
100110=>101010=>010101=>101010
100111=>010111=>111010=>000101
101000=>001100=>001100=>110011
101001=>011001=>100110=>011001
101010=>111000=>000111=>111000
101011=>110011=>110011=>001100
101100=>011010=>010110=>101001
101101=>110101=>101011=>010100
101110=>110110=>011011=>100100
101111=>101111=>111101=>000010
110000=>000110=>011000=>100111
110001=>001101=>101100=>010011
110010=>101100=>001101=>110010
110011=>011011=>110110=>001001
110100=>011100=>001110=>110001
110101=>111001=>100111=>011000
110110=>111010=>010111=>101000
110111=>110111=>111011=>000100
111000=>001110=>011100=>100011
111001=>011101=>101110=>010001
111010=>111100=>001111=>110000
111011=>111011=>110111=>001000
111100=>011110=>011110=>100001
111101=>111101=>101111=>010000
111110=>111110=>011111=>100000
111111=>111111=>111111=>000000
0000000=>0000000=>0000000=>1111111
0000001=>0000001=>1000000=>0111111
0000010=>1000000=>0000001=>1111110
0000011=>0000011=>1100000=>0011111
0000100=>0100000=>0000010=>1111101
0000101=>1000001=>1000001=>0111110
0000110=>1000010=>0100001=>1011110
0000111=>0000111=>1110000=>0001111
0001000=>0010000=>0000100=>1111011
0001001=>0100001=>1000010=>0111101
0001010=>1100000=>0000011=>1111100
0001011=>1000011=>1100001=>0011110
0001100=>0100010=>0100010=>1011101
0001101=>1000101=>1010001=>0101110
0001110=>1000110=>0110001=>1001110
0001111=>0001111=>1111000=>0000111
0010000=>0001000=>0001000=>1110111
0010001=>0010001=>1000100=>0111011
0010010=>1010000=>0000101=>1111010
0010011=>0100011=>1100010=>0011101
0010100=>0110000=>0000110=>1111001
0010101=>1100001=>1000011=>0111100
0010110=>1100010=>0100011=>1011100
0010111=>1000111=>1110001=>0001110
0011000=>0010010=>0100100=>1011011
0011001=>0100101=>1010010=>0101101
0011010=>1100100=>0010011=>1101100
0011011=>1001011=>1101001=>0010110
0011100=>0100110=>0110010=>1001101
0011101=>1001101=>1011001=>0100110
0011110=>1001110=>0111001=>1000110
0011111=>0011111=>1111100=>0000011
0100000=>0000100=>0010000=>1101111
0100001=>0001001=>1001000=>0110111
0100010=>1001000=>0001001=>1110110
0100011=>0010011=>1100100=>0011011
0100100=>0101000=>0001010=>1110101
0100101=>1010001=>1000101=>0111010
0100110=>1010010=>0100101=>1011010
0100111=>0100111=>1110010=>0001101
0101000=>0011000=>0001100=>1110011
0101001=>0110001=>1000110=>0111001
0101010=>1110000=>0000111=>1111000
0101011=>1100011=>1100011=>0011100
0101100=>0110010=>0100110=>1011001
0101101=>1100101=>1010011=>0101100
0101110=>1100110=>0110011=>1001100
0101111=>1001111=>1111001=>0000110
0110000=>0001010=>0101000=>1010111
0110001=>0010101=>1010100=>0101011
0110010=>1010100=>0010101=>1101010
0110011=>0101011=>1101010=>0010101
0110100=>0110100=>0010110=>1101001
0110101=>1101001=>1001011=>0110100
0110110=>1101010=>0101011=>1010100
0110111=>1010111=>1110101=>0001010
0111000=>0010110=>0110100=>1001011
0111001=>0101101=>1011010=>0100101
0111010=>1101100=>0011011=>1100100
0111011=>1011011=>1101101=>0010010
0111100=>0101110=>0111010=>1000101
0111101=>1011101=>1011101=>0100010
0111110=>1011110=>0111101=>1000010
0111111=>0111111=>1111110=>0000001
1000000=>0000010=>0100000=>1011111
1000001=>0000101=>1010000=>0101111
1000010=>1000100=>0010001=>1101110
1000011=>0001011=>1101000=>0010111
1000100=>0100100=>0010010=>1101101
1000101=>1001001=>1001001=>0110110
1000110=>1001010=>0101001=>1010110
1000111=>0010111=>1110100=>0001011
1001000=>0010100=>0010100=>1101011
1001001=>0101001=>1001010=>0110101
1001010=>1101000=>0001011=>1110100
1001011=>1010011=>1100101=>0011010
1001100=>0101010=>0101010=>1010101
1001101=>1010101=>1010101=>0101010
1001110=>1010110=>0110101=>1001010
1001111=>0101111=>1111010=>0000101
1010000=>0001100=>0011000=>1100111
1010001=>0011001=>1001100=>0110011
1010010=>1011000=>0001101=>1110010
1010011=>0110011=>1100110=>0011001
1010100=>0111000=>0001110=>1110001
1010101=>1110001=>1000111=>0111000
1010110=>1110010=>0100111=>1011000
1010111=>1100111=>1110011=>0001100
1011000=>0011010=>0101100=>1010011
1011001=>0110101=>1010110=>0101001
1011010=>1110100=>0010111=>1101000
1011011=>1101011=>1101011=>0010100
1011100=>0110110=>0110110=>1001001
1011101=>1101101=>1011011=>0100100
1011110=>1101110=>0111011=>1000100
1011111=>1011111=>1111101=>0000010
1100000=>0000110=>0110000=>1001111
1100001=>0001101=>1011000=>0100111
1100010=>1001100=>0011001=>1100110
1100011=>0011011=>1101100=>0010011
1100100=>0101100=>0011010=>1100101
1100101=>1011001=>1001101=>0110010
1100110=>1011010=>0101101=>1010010
1100111=>0110111=>1110110=>0001001
1101000=>0011100=>0011100=>1100011
1101001=>0111001=>1001110=>0110001
1101010=>1111000=>0001111=>1110000
1101011=>1110011=>1100111=>0011000
1101100=>0111010=>0101110=>1010001
1101101=>1110101=>1010111=>0101000
1101110=>1110110=>0110111=>1001000
1101111=>1101111=>1111011=>0000100
1110000=>0001110=>0111000=>1000111
1110001=>0011101=>1011100=>0100011
1110010=>1011100=>0011101=>1100010
1110011=>0111011=>1101110=>0010001
1110100=>0111100=>0011110=>1100001
1110101=>1111001=>1001111=>0110000
1110110=>1111010=>0101111=>1010000
1110111=>1110111=>1110111=>0001000
1111000=>0011110=>0111100=>1000011
1111001=>0111101=>1011110=>0100001
1111010=>1111100=>0011111=>1100000
1111011=>1111011=>1101111=>0010000
1111100=>0111110=>0111110=>1000001
1111101=>1111101=>1011111=>0100000
1111110=>1111110=>0111111=>1000000
1111111=>1111111=>1111111=>0000000
00000000=>00000000=>00000000=>11111111
00000001=>00000001=>10000000=>01111111
00000010=>10000000=>00000001=>11111110
00000011=>00000011=>11000000=>00111111
00000100=>01000000=>00000010=>11111101
00000101=>10000001=>10000001=>01111110
00000110=>10000010=>01000001=>10111110
00000111=>00000111=>11100000=>00011111
00001000=>00100000=>00000100=>11111011
00001001=>01000001=>10000010=>01111101
00001010=>11000000=>00000011=>11111100
00001011=>10000011=>11000001=>00111110
00001100=>01000010=>01000010=>10111101
00001101=>10000101=>10100001=>01011110
00001110=>10000110=>01100001=>10011110
00001111=>00001111=>11110000=>00001111
00010000=>00010000=>00001000=>11110111
00010001=>00100001=>10000100=>01111011
00010010=>10100000=>00000101=>11111010
00010011=>01000011=>11000010=>00111101
00010100=>01100000=>00000110=>11111001
00010101=>11000001=>10000011=>01111100
00010110=>11000010=>01000011=>10111100
00010111=>10000111=>11100001=>00011110
00011000=>00100010=>01000100=>10111011
00011001=>01000101=>10100010=>01011101
00011010=>11000100=>00100011=>11011100
00011011=>10001011=>11010001=>00101110
00011100=>01000110=>01100010=>10011101
00011101=>10001101=>10110001=>01001110
00011110=>10001110=>01110001=>10001110
00011111=>00011111=>11111000=>00000111
00100000=>00001000=>00010000=>11101111
00100001=>00010001=>10001000=>01110111
00100010=>10010000=>00001001=>11110110
00100011=>00100011=>11000100=>00111011
00100100=>01010000=>00001010=>11110101
00100101=>10100001=>10000101=>01111010
00100110=>10100010=>01000101=>10111010
00100111=>01000111=>11100010=>00011101
00101000=>00110000=>00001100=>11110011
00101001=>01100001=>10000110=>01111001
00101010=>11100000=>00000111=>11111000
00101011=>11000011=>11000011=>00111100
00101100=>01100010=>01000110=>10111001
00101101=>11000101=>10100011=>01011100
00101110=>11000110=>01100011=>10011100
00101111=>10001111=>11110001=>00001110
00110000=>00010010=>01001000=>10110111
00110001=>00100101=>10100100=>01011011
00110010=>10100100=>00100101=>11011010
00110011=>01001011=>11010010=>00101101
00110100=>01100100=>00100110=>11011001
00110101=>11001001=>10010011=>01101100
00110110=>11001010=>01010011=>10101100
00110111=>10010111=>11101001=>00010110
00111000=>00100110=>01100100=>10011011
00111001=>01001101=>10110010=>01001101
00111010=>11001100=>00110011=>11001100
00111011=>10011011=>11011001=>00100110
00111100=>01001110=>01110010=>10001101
00111101=>10011101=>10111001=>01000110
00111110=>10011110=>01111001=>10000110
00111111=>00111111=>11111100=>00000011
01000000=>00000100=>00100000=>11011111
01000001=>00001001=>10010000=>01101111
01000010=>10001000=>00010001=>11101110
01000011=>00010011=>11001000=>00110111
01000100=>01001000=>00010010=>11101101
01000101=>10010001=>10001001=>01110110
01000110=>10010010=>01001001=>10110110
01000111=>00100111=>11100100=>00011011
01001000=>00101000=>00010100=>11101011
01001001=>01010001=>10001010=>01110101
01001010=>11010000=>00001011=>11110100
01001011=>10100011=>11000101=>00111010
01001100=>01010010=>01001010=>10110101
01001101=>10100101=>10100101=>01011010
01001110=>10100110=>01100101=>10011010
01001111=>01001111=>11110010=>00001101
01010000=>00011000=>00011000=>11100111
01010001=>00110001=>10001100=>01110011
01010010=>10110000=>00001101=>11110010
01010011=>01100011=>11000110=>00111001
01010100=>01110000=>00001110=>11110001
01010101=>11100001=>10000111=>01111000
01010110=>11100010=>01000111=>10111000
01010111=>11000111=>11100011=>00011100
01011000=>00110010=>01001100=>10110011
01011001=>01100101=>10100110=>01011001
01011010=>11100100=>00100111=>11011000
01011011=>11001011=>11010011=>00101100
01011100=>01100110=>01100110=>10011001
01011101=>11001101=>10110011=>01001100
01011110=>11001110=>01110011=>10001100
01011111=>10011111=>11111001=>00000110
01100000=>00001010=>01010000=>10101111
01100001=>00010101=>10101000=>01010111
01100010=>10010100=>00101001=>11010110
01100011=>00101011=>11010100=>00101011
01100100=>01010100=>00101010=>11010101
01100101=>10101001=>10010101=>01101010
01100110=>10101010=>01010101=>10101010
01100111=>01010111=>11101010=>00010101
01101000=>00110100=>00101100=>11010011
01101001=>01101001=>10010110=>01101001
01101010=>11101000=>00010111=>11101000
01101011=>11010011=>11001011=>00110100
01101100=>01101010=>01010110=>10101001
01101101=>11010101=>10101011=>01010100
01101110=>11010110=>01101011=>10010100
01101111=>10101111=>11110101=>00001010
01110000=>00010110=>01101000=>10010111
01110001=>00101101=>10110100=>01001011
01110010=>10101100=>00110101=>11001010
01110011=>01011011=>11011010=>00100101
01110100=>01101100=>00110110=>11001001
01110101=>11011001=>10011011=>01100100
01110110=>11011010=>01011011=>10100100
01110111=>10110111=>11101101=>00010010
01111000=>00101110=>01110100=>10001011
01111001=>01011101=>10111010=>01000101
01111010=>11011100=>00111011=>11000100
01111011=>10111011=>11011101=>00100010
01111100=>01011110=>01111010=>10000101
01111101=>10111101=>10111101=>01000010
01111110=>10111110=>01111101=>10000010
01111111=>01111111=>11111110=>00000001
10000000=>00000010=>01000000=>10111111
10000001=>00000101=>10100000=>01011111
10000010=>10000100=>00100001=>11011110
10000011=>00001011=>11010000=>00101111
10000100=>01000100=>00100010=>11011101
10000101=>10001001=>10010001=>01101110
10000110=>10001010=>01010001=>10101110
10000111=>00010111=>11101000=>00010111
10001000=>00100100=>00100100=>11011011
10001001=>01001001=>10010010=>01101101
10001010=>11001000=>00010011=>11101100
10001011=>10010011=>11001001=>00110110
10001100=>01001010=>01010010=>10101101
10001101=>10010101=>10101001=>01010110
10001110=>10010110=>01101001=>10010110
10001111=>00101111=>11110100=>00001011
10010000=>00010100=>00101000=>11010111
10010001=>00101001=>10010100=>01101011
10010010=>10101000=>00010101=>11101010
10010011=>01010011=>11001010=>00110101
10010100=>01101000=>00010110=>11101001
10010101=>11010001=>10001011=>01110100
10010110=>11010010=>01001011=>10110100
10010111=>10100111=>11100101=>00011010
10011000=>00101010=>01010100=>10101011
10011001=>01010101=>10101010=>01010101
10011010=>11010100=>00101011=>11010100
10011011=>10101011=>11010101=>00101010
10011100=>01010110=>01101010=>10010101
10011101=>10101101=>10110101=>01001010
10011110=>10101110=>01110101=>10001010
10011111=>01011111=>11111010=>00000101
10100000=>00001100=>00110000=>11001111
10100001=>00011001=>10011000=>01100111
10100010=>10011000=>00011001=>11100110
10100011=>00110011=>11001100=>00110011
10100100=>01011000=>00011010=>11100101
10100101=>10110001=>10001101=>01110010
10100110=>10110010=>01001101=>10110010
10100111=>01100111=>11100110=>00011001
10101000=>00111000=>00011100=>11100011
10101001=>01110001=>10001110=>01110001
10101010=>11110000=>00001111=>11110000
10101011=>11100011=>11000111=>00111000
10101100=>01110010=>01001110=>10110001
10101101=>11100101=>10100111=>01011000
10101110=>11100110=>01100111=>10011000
10101111=>11001111=>11110011=>00001100
10110000=>00011010=>01011000=>10100111
10110001=>00110101=>10101100=>01010011
10110010=>10110100=>00101101=>11010010
10110011=>01101011=>11010110=>00101001
10110100=>01110100=>00101110=>11010001
10110101=>11101001=>10010111=>01101000
10110110=>11101010=>01010111=>10101000
10110111=>11010111=>11101011=>00010100
10111000=>00110110=>01101100=>10010011
10111001=>01101101=>10110110=>01001001
10111010=>11101100=>00110111=>11001000
10111011=>11011011=>11011011=>00100100
10111100=>01101110=>01110110=>10001001
10111101=>11011101=>10111011=>01000100
10111110=>11011110=>01111011=>10000100
10111111=>10111111=>11111101=>00000010
11000000=>00000110=>01100000=>10011111
11000001=>00001101=>10110000=>01001111
11000010=>10001100=>00110001=>11001110
11000011=>00011011=>11011000=>00100111
11000100=>01001100=>00110010=>11001101
11000101=>10011001=>10011001=>01100110
11000110=>10011010=>01011001=>10100110
11000111=>00110111=>11101100=>00010011
11001000=>00101100=>00110100=>11001011
11001001=>01011001=>10011010=>01100101
11001010=>11011000=>00011011=>11100100
11001011=>10110011=>11001101=>00110010
11001100=>01011010=>01011010=>10100101
11001101=>10110101=>10101101=>01010010
11001110=>10110110=>01101101=>10010010
11001111=>01101111=>11110110=>00001001
11010000=>00011100=>00111000=>11000111
11010001=>00111001=>10011100=>01100011
11010010=>10111000=>00011101=>11100010
11010011=>01110011=>11001110=>00110001
11010100=>01111000=>00011110=>11100001
11010101=>11110001=>10001111=>01110000
11010110=>11110010=>01001111=>10110000
11010111=>11100111=>11100111=>00011000
11011000=>00111010=>01011100=>10100011
11011001=>01110101=>10101110=>01010001
11011010=>11110100=>00101111=>11010000
11011011=>11101011=>11010111=>00101000
11011100=>01110110=>01101110=>10010001
11011101=>11101101=>10110111=>01001000
11011110=>11101110=>01110111=>10001000
11011111=>11011111=>11111011=>00000100
11100000=>00001110=>01110000=>10001111
11100001=>00011101=>10111000=>01000111
11100010=>10011100=>00111001=>11000110
11100011=>00111011=>11011100=>00100011
11100100=>01011100=>00111010=>11000101
11100101=>10111001=>10011101=>01100010
11100110=>10111010=>01011101=>10100010
11100111=>01110111=>11101110=>00010001
11101000=>00111100=>00111100=>11000011
11101001=>01111001=>10011110=>01100001
11101010=>11111000=>00011111=>11100000
11101011=>11110011=>11001111=>00110000
11101100=>01111010=>01011110=>10100001
11101101=>11110101=>10101111=>01010000
11101110=>11110110=>01101111=>10010000
11101111=>11101111=>11110111=>00001000
11110000=>00011110=>01111000=>10000111
11110001=>00111101=>10111100=>01000011
11110010=>10111100=>00111101=>11000010
11110011=>01111011=>11011110=>00100001
11110100=>01111100=>00111110=>11000001
11110101=>11111001=>10011111=>01100000
11110110=>11111010=>01011111=>10100000
11110111=>11110111=>11101111=>00010000
11111000=>00111110=>01111100=>10000011
11111001=>01111101=>10111110=>01000001
11111010=>11111100=>00111111=>11000000
11111011=>11111011=>11011111=>00100000
11111100=>01111110=>01111110=>10000001
11111101=>11111101=>10111111=>01000000
11111110=>11111110=>01111111=>10000000
11111111=>11111111=>11111111=>00000000
000000000=>000000000=>000000000=>111111111
000000001=>000000001=>100000000=>011111111
000000010=>100000000=>000000001=>111111110
000000011=>000000011=>110000000=>001111111
000000100=>010000000=>000000010=>111111101
000000101=>100000001=>100000001=>011111110
000000110=>100000010=>010000001=>101111110
000000111=>000000111=>111000000=>000111111
000001000=>001000000=>000000100=>111111011
000001001=>010000001=>100000010=>011111101
000001010=>110000000=>000000011=>111111100
000001011=>100000011=>110000001=>001111110
000001100=>010000010=>010000010=>101111101
000001101=>100000101=>101000001=>010111110
000001110=>100000110=>011000001=>100111110
000001111=>000001111=>111100000=>000011111
000010000=>000100000=>000001000=>111110111
000010001=>001000001=>100000100=>011111011
000010010=>101000000=>000000101=>111111010
000010011=>010000011=>110000010=>001111101
000010100=>011000000=>000000110=>111111001
000010101=>110000001=>100000011=>011111100
000010110=>110000010=>010000011=>101111100
000010111=>100000111=>111000001=>000111110
000011000=>001000010=>010000100=>101111011
000011001=>010000101=>101000010=>010111101
000011010=>110000100=>001000011=>110111100
000011011=>100001011=>110100001=>001011110
000011100=>010000110=>011000010=>100111101
000011101=>100001101=>101100001=>010011110
000011110=>100001110=>011100001=>100011110
000011111=>000011111=>111110000=>000001111
000100000=>000010000=>000010000=>111101111
000100001=>000100001=>100001000=>011110111
000100010=>100100000=>000001001=>111110110
000100011=>001000011=>110000100=>001111011
000100100=>010100000=>000001010=>111110101
000100101=>101000001=>100000101=>011111010
000100110=>101000010=>010000101=>101111010
000100111=>010000111=>111000010=>000111101
000101000=>001100000=>000001100=>111110011
000101001=>011000001=>100000110=>011111001
000101010=>111000000=>000000111=>111111000
000101011=>110000011=>110000011=>001111100
000101100=>011000010=>010000110=>101111001
000101101=>110000101=>101000011=>010111100
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011101010011=>011101100011=>110001101110=>001110010001
011100110101=>110101101001=>100101101011=>011010010100
001111010101=>111001110001=>100011100111=>011100011000
110110000111=>000111010111=>111010111000=>000101000111
111000011101=>100011101101=>101101110001=>010010001110
011101101001=>011101101001=>100101101110=>011010010001
011101011001=>011101100101=>101001101110=>010110010001
011110010101=>110101110001=>100011101011=>011100010100
011110101001=>011101110001=>100011101110=>011100010001
011110100011=>001101110011=>110011101100=>001100010011
011111000101=>100101111001=>100111101001=>011000010110
00001101111=>10000101111=>11110100001=>00001011110
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.
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