Identifier
Mp00105:
Binary words
—complement⟶
Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Images
=>
0=>1=>1
1=>0=>0
00=>11=>11
01=>10=>10
10=>01=>01
11=>00=>00
000=>111=>111
001=>110=>110
010=>101=>101
011=>100=>010
100=>011=>011
101=>010=>100
110=>001=>001
111=>000=>000
0000=>1111=>1111
0001=>1110=>1110
0010=>1101=>1101
0011=>1100=>0110
0100=>1011=>1011
0101=>1010=>1100
0110=>1001=>0101
0111=>1000=>0010
1000=>0111=>0111
1001=>0110=>1010
1010=>0101=>1001
1011=>0100=>0100
1100=>0011=>0011
1101=>0010=>1000
1110=>0001=>0001
1111=>0000=>0000
00000=>11111=>11111
00001=>11110=>11110
00010=>11101=>11101
00011=>11100=>01110
00100=>11011=>11011
00101=>11010=>11100
00110=>11001=>01101
00111=>11000=>00110
01000=>10111=>10111
01001=>10110=>11010
01010=>10101=>11001
01011=>10100=>01100
01100=>10011=>01011
01101=>10010=>10100
01110=>10001=>00101
01111=>10000=>00010
10000=>01111=>01111
10001=>01110=>10110
10010=>01101=>10101
10011=>01100=>01010
10100=>01011=>10011
10101=>01010=>11000
10110=>01001=>01001
10111=>01000=>00100
11000=>00111=>00111
11001=>00110=>10010
11010=>00101=>10001
11011=>00100=>01000
11100=>00011=>00011
11101=>00010=>10000
11110=>00001=>00001
11111=>00000=>00000
000000=>111111=>111111
000001=>111110=>111110
000010=>111101=>111101
000011=>111100=>011110
000100=>111011=>111011
000101=>111010=>111100
000110=>111001=>011101
000111=>111000=>001110
001000=>110111=>110111
001001=>110110=>111010
001010=>110101=>111001
001011=>110100=>011100
001100=>110011=>011011
001101=>110010=>101100
001110=>110001=>001101
001111=>110000=>000110
010000=>101111=>101111
010001=>101110=>110110
010010=>101101=>110101
010011=>101100=>011010
010100=>101011=>110011
010101=>101010=>111000
010110=>101001=>011001
010111=>101000=>001100
011000=>100111=>010111
011001=>100110=>101010
011010=>100101=>101001
011011=>100100=>010100
011100=>100011=>001011
011101=>100010=>100100
011110=>100001=>000101
011111=>100000=>000010
100000=>011111=>011111
100001=>011110=>101110
100010=>011101=>101101
100011=>011100=>010110
100100=>011011=>101011
100101=>011010=>110100
100110=>011001=>010101
100111=>011000=>001010
101000=>010111=>100111
101001=>010110=>110010
101010=>010101=>110001
101011=>010100=>011000
101100=>010011=>010011
101101=>010010=>101000
101110=>010001=>001001
101111=>010000=>000100
110000=>001111=>001111
110001=>001110=>100110
110010=>001101=>100101
110011=>001100=>010010
110100=>001011=>100011
110101=>001010=>110000
110110=>001001=>010001
110111=>001000=>001000
111000=>000111=>000111
111001=>000110=>100010
111010=>000101=>100001
111011=>000100=>010000
111100=>000011=>000011
111101=>000010=>100000
111110=>000001=>000001
111111=>000000=>000000
0000000=>1111111=>1111111
0000001=>1111110=>1111110
0000010=>1111101=>1111101
0000011=>1111100=>0111110
0000100=>1111011=>1111011
0000101=>1111010=>1111100
0000110=>1111001=>0111101
0000111=>1111000=>0011110
0001000=>1110111=>1110111
0001001=>1110110=>1111010
0001010=>1110101=>1111001
0001011=>1110100=>0111100
0001100=>1110011=>0111011
0001101=>1110010=>1011100
0001110=>1110001=>0011101
0001111=>1110000=>0001110
0010000=>1101111=>1101111
0010001=>1101110=>1110110
0010010=>1101101=>1110101
0010011=>1101100=>0111010
0010100=>1101011=>1110011
0010101=>1101010=>1111000
0010110=>1101001=>0111001
0010111=>1101000=>0011100
0011000=>1100111=>0110111
0011001=>1100110=>1011010
0011010=>1100101=>1011001
0011011=>1100100=>0101100
0011100=>1100011=>0011011
0011101=>1100010=>1001100
0011110=>1100001=>0001101
0011111=>1100000=>0000110
0100000=>1011111=>1011111
0100001=>1011110=>1101110
0100010=>1011101=>1101101
0100011=>1011100=>0110110
0100100=>1011011=>1101011
0100101=>1011010=>1110100
0100110=>1011001=>0110101
0100111=>1011000=>0011010
0101000=>1010111=>1100111
0101001=>1010110=>1110010
0101010=>1010101=>1110001
0101011=>1010100=>0111000
0101100=>1010011=>0110011
0101101=>1010010=>1011000
0101110=>1010001=>0011001
0101111=>1010000=>0001100
0110000=>1001111=>0101111
0110001=>1001110=>1010110
0110010=>1001101=>1010101
0110011=>1001100=>0101010
0110100=>1001011=>1010011
0110101=>1001010=>1101000
0110110=>1001001=>0101001
0110111=>1001000=>0010100
0111000=>1000111=>0010111
0111001=>1000110=>1001010
0111010=>1000101=>1001001
0111011=>1000100=>0100100
0111100=>1000011=>0001011
0111101=>1000010=>1000100
0111110=>1000001=>0000101
0111111=>1000000=>0000010
1000000=>0111111=>0111111
1000001=>0111110=>1011110
1000010=>0111101=>1011101
1000011=>0111100=>0101110
1000100=>0111011=>1011011
1000101=>0111010=>1101100
1000110=>0111001=>0101101
1000111=>0111000=>0010110
1001000=>0110111=>1010111
1001001=>0110110=>1101010
1001010=>0110101=>1101001
1001011=>0110100=>0110100
1001100=>0110011=>0101011
1001101=>0110010=>1010100
1001110=>0110001=>0010101
1001111=>0110000=>0001010
1010000=>0101111=>1001111
1010001=>0101110=>1100110
1010010=>0101101=>1100101
1010011=>0101100=>0110010
1010100=>0101011=>1100011
1010101=>0101010=>1110000
1010110=>0101001=>0110001
1010111=>0101000=>0011000
1011000=>0100111=>0100111
1011001=>0100110=>1010010
1011010=>0100101=>1010001
1011011=>0100100=>0101000
1011100=>0100011=>0010011
1011101=>0100010=>1001000
1011110=>0100001=>0001001
1011111=>0100000=>0000100
1100000=>0011111=>0011111
1100001=>0011110=>1001110
1100010=>0011101=>1001101
1100011=>0011100=>0100110
1100100=>0011011=>1001011
1100101=>0011010=>1100100
1100110=>0011001=>0100101
1100111=>0011000=>0010010
1101000=>0010111=>1000111
1101001=>0010110=>1100010
1101010=>0010101=>1100001
1101011=>0010100=>0110000
1101100=>0010011=>0100011
1101101=>0010010=>1010000
1101110=>0010001=>0010001
1101111=>0010000=>0001000
1110000=>0001111=>0001111
1110001=>0001110=>1000110
1110010=>0001101=>1000101
1110011=>0001100=>0100010
1110100=>0001011=>1000011
1110101=>0001010=>1100000
1110110=>0001001=>0100001
1110111=>0001000=>0010000
1111000=>0000111=>0000111
1111001=>0000110=>1000010
1111010=>0000101=>1000001
1111011=>0000100=>0100000
1111100=>0000011=>0000011
1111101=>0000010=>1000000
1111110=>0000001=>0000001
1111111=>0000000=>0000000
00000000=>11111111=>11111111
00000001=>11111110=>11111110
00000010=>11111101=>11111101
00000011=>11111100=>01111110
00000100=>11111011=>11111011
00000101=>11111010=>11111100
00000110=>11111001=>01111101
00000111=>11111000=>00111110
00001000=>11110111=>11110111
00001001=>11110110=>11111010
00001010=>11110101=>11111001
00001011=>11110100=>01111100
00001100=>11110011=>01111011
00001101=>11110010=>10111100
00001110=>11110001=>00111101
00001111=>11110000=>00011110
00010000=>11101111=>11101111
00010001=>11101110=>11110110
00010010=>11101101=>11110101
00010011=>11101100=>01111010
00010100=>11101011=>11110011
00010101=>11101010=>11111000
00010110=>11101001=>01111001
00010111=>11101000=>00111100
00011000=>11100111=>01110111
00011001=>11100110=>10111010
00011010=>11100101=>10111001
00011011=>11100100=>01011100
00011100=>11100011=>00111011
00011101=>11100010=>10011100
00011110=>11100001=>00011101
00011111=>11100000=>00001110
00100000=>11011111=>11011111
00100001=>11011110=>11101110
00100010=>11011101=>11101101
00100011=>11011100=>01110110
00100100=>11011011=>11101011
00100101=>11011010=>11110100
00100110=>11011001=>01110101
00100111=>11011000=>00111010
00101000=>11010111=>11100111
00101001=>11010110=>11110010
00101010=>11010101=>11110001
00101011=>11010100=>01111000
00101100=>11010011=>01110011
00101101=>11010010=>10111000
00101110=>11010001=>00111001
00101111=>11010000=>00011100
00110000=>11001111=>01101111
00110001=>11001110=>10110110
00110010=>11001101=>10110101
00110011=>11001100=>01011010
00110100=>11001011=>10110011
00110101=>11001010=>11011000
00110110=>11001001=>01011001
00110111=>11001000=>00101100
00111000=>11000111=>00110111
00111001=>11000110=>10011010
00111010=>11000101=>10011001
00111011=>11000100=>01001100
00111100=>11000011=>00011011
00111101=>11000010=>10001100
00111110=>11000001=>00001101
00111111=>11000000=>00000110
01000000=>10111111=>10111111
01000001=>10111110=>11011110
01000010=>10111101=>11011101
01000011=>10111100=>01101110
01000100=>10111011=>11011011
01000101=>10111010=>11101100
01000110=>10111001=>01101101
01000111=>10111000=>00110110
01001000=>10110111=>11010111
01001001=>10110110=>11101010
01001010=>10110101=>11101001
01001011=>10110100=>01110100
01001100=>10110011=>01101011
01001101=>10110010=>10110100
01001110=>10110001=>00110101
01001111=>10110000=>00011010
01010000=>10101111=>11001111
01010001=>10101110=>11100110
01010010=>10101101=>11100101
01010011=>10101100=>01110010
01010100=>10101011=>11100011
01010101=>10101010=>11110000
01010110=>10101001=>01110001
01010111=>10101000=>00111000
01011000=>10100111=>01100111
01011001=>10100110=>10110010
01011010=>10100101=>10110001
01011011=>10100100=>01011000
01011100=>10100011=>00110011
01011101=>10100010=>10011000
01011110=>10100001=>00011001
01011111=>10100000=>00001100
01100000=>10011111=>01011111
01100001=>10011110=>10101110
01100010=>10011101=>10101101
01100011=>10011100=>01010110
01100100=>10011011=>10101011
01100101=>10011010=>11010100
01100110=>10011001=>01010101
01100111=>10011000=>00101010
01101000=>10010111=>10100111
01101001=>10010110=>11010010
01101010=>10010101=>11010001
01101011=>10010100=>01101000
01101100=>10010011=>01010011
01101101=>10010010=>10101000
01101110=>10010001=>00101001
01101111=>10010000=>00010100
01110000=>10001111=>00101111
01110001=>10001110=>10010110
01110010=>10001101=>10010101
01110011=>10001100=>01001010
01110100=>10001011=>10010011
01110101=>10001010=>11001000
01110110=>10001001=>01001001
01110111=>10001000=>00100100
01111000=>10000111=>00010111
01111001=>10000110=>10001010
01111010=>10000101=>10001001
01111011=>10000100=>01000100
01111100=>10000011=>00001011
01111101=>10000010=>10000100
01111110=>10000001=>00000101
01111111=>10000000=>00000010
10000000=>01111111=>01111111
10000001=>01111110=>10111110
10000010=>01111101=>10111101
10000011=>01111100=>01011110
10000100=>01111011=>10111011
10000101=>01111010=>11011100
10000110=>01111001=>01011101
10000111=>01111000=>00101110
10001000=>01110111=>10110111
10001001=>01110110=>11011010
10001010=>01110101=>11011001
10001011=>01110100=>01101100
10001100=>01110011=>01011011
10001101=>01110010=>10101100
10001110=>01110001=>00101101
10001111=>01110000=>00010110
10010000=>01101111=>10101111
10010001=>01101110=>11010110
10010010=>01101101=>11010101
10010011=>01101100=>01101010
10010100=>01101011=>11010011
10010101=>01101010=>11101000
10010110=>01101001=>01101001
10010111=>01101000=>00110100
10011000=>01100111=>01010111
10011001=>01100110=>10101010
10011010=>01100101=>10101001
10011011=>01100100=>01010100
10011100=>01100011=>00101011
10011101=>01100010=>10010100
10011110=>01100001=>00010101
10011111=>01100000=>00001010
10100000=>01011111=>10011111
10100001=>01011110=>11001110
10100010=>01011101=>11001101
10100011=>01011100=>01100110
10100100=>01011011=>11001011
10100101=>01011010=>11100100
10100110=>01011001=>01100101
10100111=>01011000=>00110010
10101000=>01010111=>11000111
10101001=>01010110=>11100010
10101010=>01010101=>11100001
10101011=>01010100=>01110000
10101100=>01010011=>01100011
10101101=>01010010=>10110000
10101110=>01010001=>00110001
10101111=>01010000=>00011000
10110000=>01001111=>01001111
10110001=>01001110=>10100110
10110010=>01001101=>10100101
10110011=>01001100=>01010010
10110100=>01001011=>10100011
10110101=>01001010=>11010000
10110110=>01001001=>01010001
10110111=>01001000=>00101000
10111000=>01000111=>00100111
10111001=>01000110=>10010010
10111010=>01000101=>10010001
10111011=>01000100=>01001000
10111100=>01000011=>00010011
10111101=>01000010=>10001000
10111110=>01000001=>00001001
10111111=>01000000=>00000100
11000000=>00111111=>00111111
11000001=>00111110=>10011110
11000010=>00111101=>10011101
11000011=>00111100=>01001110
11000100=>00111011=>10011011
11000101=>00111010=>11001100
11000110=>00111001=>01001101
11000111=>00111000=>00100110
11001000=>00110111=>10010111
11001001=>00110110=>11001010
11001010=>00110101=>11001001
11001011=>00110100=>01100100
11001100=>00110011=>01001011
11001101=>00110010=>10100100
11001110=>00110001=>00100101
11001111=>00110000=>00010010
11010000=>00101111=>10001111
11010001=>00101110=>11000110
11010010=>00101101=>11000101
11010011=>00101100=>01100010
11010100=>00101011=>11000011
11010101=>00101010=>11100000
11010110=>00101001=>01100001
11010111=>00101000=>00110000
11011000=>00100111=>01000111
11011001=>00100110=>10100010
11011010=>00100101=>10100001
11011011=>00100100=>01010000
11011100=>00100011=>00100011
11011101=>00100010=>10010000
11011110=>00100001=>00010001
11011111=>00100000=>00001000
11100000=>00011111=>00011111
11100001=>00011110=>10001110
11100010=>00011101=>10001101
11100011=>00011100=>01000110
11100100=>00011011=>10001011
11100101=>00011010=>11000100
11100110=>00011001=>01000101
11100111=>00011000=>00100010
11101000=>00010111=>10000111
11101001=>00010110=>11000010
11101010=>00010101=>11000001
11101011=>00010100=>01100000
11101100=>00010011=>01000011
11101101=>00010010=>10100000
11101110=>00010001=>00100001
11101111=>00010000=>00010000
11110000=>00001111=>00001111
11110001=>00001110=>10000110
11110010=>00001101=>10000101
11110011=>00001100=>01000010
11110100=>00001011=>10000011
11110101=>00001010=>11000000
11110110=>00001001=>01000001
11110111=>00001000=>00100000
11111000=>00000111=>00000111
11111001=>00000110=>10000010
11111010=>00000101=>10000001
11111011=>00000100=>01000000
11111100=>00000011=>00000011
11111101=>00000010=>10000000
11111110=>00000001=>00000001
11111111=>00000000=>00000000
000000000=>111111111=>111111111
000000001=>111111110=>111111110
000000010=>111111101=>111111101
000000011=>111111100=>011111110
000000100=>111111011=>111111011
000000101=>111111010=>111111100
000000110=>111111001=>011111101
000000111=>111111000=>001111110
000001000=>111110111=>111110111
000001001=>111110110=>111111010
000001010=>111110101=>111111001
000001011=>111110100=>011111100
000001100=>111110011=>011111011
000001101=>111110010=>101111100
000001110=>111110001=>001111101
000001111=>111110000=>000111110
000010000=>111101111=>111101111
000010001=>111101110=>111110110
000010010=>111101101=>111110101
000010011=>111101100=>011111010
000010100=>111101011=>111110011
000010101=>111101010=>111111000
000010110=>111101001=>011111001
000010111=>111101000=>001111100
000011000=>111100111=>011110111
000011001=>111100110=>101111010
000011010=>111100101=>101111001
000011011=>111100100=>010111100
000011100=>111100011=>001111011
000011101=>111100010=>100111100
000011110=>111100001=>000111101
000011111=>111100000=>000011110
000100000=>111011111=>111011111
000100001=>111011110=>111101110
000100010=>111011101=>111101101
000100011=>111011100=>011110110
000100100=>111011011=>111101011
000100101=>111011010=>111110100
000100110=>111011001=>011110101
000100111=>111011000=>001111010
000101000=>111010111=>111100111
000101001=>111010110=>111110010
000101010=>111010101=>111110001
000101011=>111010100=>011111000
000101100=>111010011=>011110011
000101101=>111010010=>101111000
000101110=>111010001=>001111001
000101111=>111010000=>000111100
000110000=>111001111=>011101111
000110001=>111001110=>101110110
000110010=>111001101=>101110101
000110011=>111001100=>010111010
000110100=>111001011=>101110011
000110101=>111001010=>110111000
000110110=>111001001=>010111001
000110111=>111001000=>001011100
000111000=>111000111=>001110111
000111001=>111000110=>100111010
000111010=>111000101=>100111001
000111011=>111000100=>010011100
000111100=>111000011=>000111011
000111101=>111000010=>100011100
000111110=>111000001=>000011101
000111111=>111000000=>000001110
001000000=>110111111=>110111111
001000001=>110111110=>111011110
001000010=>110111101=>111011101
001000011=>110111100=>011101110
001000100=>110111011=>111011011
001000101=>110111010=>111101100
001000110=>110111001=>011101101
001000111=>110111000=>001110110
001001000=>110110111=>111010111
001001001=>110110110=>111101010
001001010=>110110101=>111101001
001001011=>110110100=>011110100
001001100=>110110011=>011101011
001001101=>110110010=>101110100
001001110=>110110001=>001110101
001001111=>110110000=>000111010
001010000=>110101111=>111001111
001010001=>110101110=>111100110
001010010=>110101101=>111100101
001010011=>110101100=>011110010
001010100=>110101011=>111100011
001010101=>110101010=>111110000
001010110=>110101001=>011110001
001010111=>110101000=>001111000
001011000=>110100111=>011100111
001011001=>110100110=>101110010
001011010=>110100101=>101110001
001011011=>110100100=>010111000
001011100=>110100011=>001110011
001011101=>110100010=>100111000
001011110=>110100001=>000111001
001011111=>110100000=>000011100
001100000=>110011111=>011011111
001100001=>110011110=>101101110
001100010=>110011101=>101101101
001100011=>110011100=>010110110
001100100=>110011011=>101101011
001100101=>110011010=>110110100
001100110=>110011001=>010110101
001100111=>110011000=>001011010
001101000=>110010111=>101100111
001101001=>110010110=>110110010
001101010=>110010101=>110110001
001101011=>110010100=>011011000
001101100=>110010011=>010110011
001101101=>110010010=>101011000
001101110=>110010001=>001011001
001101111=>110010000=>000101100
001110000=>110001111=>001101111
001110001=>110001110=>100110110
001110010=>110001101=>100110101
001110011=>110001100=>010011010
001110100=>110001011=>100110011
001110101=>110001010=>110011000
001110110=>110001001=>010011001
001110111=>110001000=>001001100
001111000=>110000111=>000110111
001111001=>110000110=>100011010
001111010=>110000101=>100011001
001111011=>110000100=>010001100
001111100=>110000011=>000011011
001111101=>110000010=>100001100
001111110=>110000001=>000001101
001111111=>110000000=>000000110
010000000=>101111111=>101111111
010000001=>101111110=>110111110
010000010=>101111101=>110111101
010000011=>101111100=>011011110
010000100=>101111011=>110111011
010000101=>101111010=>111011100
010000110=>101111001=>011011101
010000111=>101111000=>001101110
010001000=>101110111=>110110111
010001001=>101110110=>111011010
010001010=>101110101=>111011001
010001011=>101110100=>011101100
010001100=>101110011=>011011011
010001101=>101110010=>101101100
010001110=>101110001=>001101101
010001111=>101110000=>000110110
010010000=>101101111=>110101111
010010001=>101101110=>111010110
010010010=>101101101=>111010101
010010011=>101101100=>011101010
010010100=>101101011=>111010011
010010101=>101101010=>111101000
010010110=>101101001=>011101001
010010111=>101101000=>001110100
010011000=>101100111=>011010111
010011001=>101100110=>101101010
010011010=>101100101=>101101001
010011011=>101100100=>010110100
010011100=>101100011=>001101011
010011101=>101100010=>100110100
010011110=>101100001=>000110101
010011111=>101100000=>000011010
010100000=>101011111=>110011111
010100001=>101011110=>111001110
010100010=>101011101=>111001101
010100011=>101011100=>011100110
010100100=>101011011=>111001011
010100101=>101011010=>111100100
010100110=>101011001=>011100101
010100111=>101011000=>001110010
010101000=>101010111=>111000111
010101001=>101010110=>111100010
010101010=>101010101=>111100001
010101011=>101010100=>011110000
010101100=>101010011=>011100011
010101101=>101010010=>101110000
010101110=>101010001=>001110001
010101111=>101010000=>000111000
010110000=>101001111=>011001111
010110001=>101001110=>101100110
010110010=>101001101=>101100101
010110011=>101001100=>010110010
010110100=>101001011=>101100011
010110101=>101001010=>110110000
010110110=>101001001=>010110001
010110111=>101001000=>001011000
010111000=>101000111=>001100111
010111001=>101000110=>100110010
010111010=>101000101=>100110001
010111011=>101000100=>010011000
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110101010101=>001010101010=>111110000000
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101100100011=>010011011100=>011010010110
111000100011=>000111011100=>011000110110
010001011110=>101110100001=>000111011001
0111111100=>1000000011=>0000001011
0010000000=>1101111111=>1101111111
0111111010=>1000000101=>1000001001
101101010101=>010010101010=>111101000000
110011010101=>001100101010=>111010010000
101011010101=>010100101010=>111011000000
100111010101=>011000101010=>111001010000
110100110101=>001011001010=>110110001000
101100110101=>010011001010=>110101001000
110010110101=>001101001010=>110110010000
101010110101=>010101001010=>110111000000
100110110101=>011001001010=>110101010000
110001110101=>001110001010=>110010011000
101001110101=>010110001010=>110011001000
100101110101=>011010001010=>110011010000
100011110101=>011100001010=>110001011000
110101001101=>001010110010=>101110000100
101101001101=>010010110010=>101101000100
110011001101=>001100110010=>101010010100
101011001101=>010100110010=>101011000100
100111001101=>011000110010=>101001010100
110100101101=>001011010010=>101110001000
101100101101=>010011010010=>101101001000
110010101101=>001101010010=>101110010000
101010101101=>010101010010=>101111000000
100110101101=>011001010010=>101101010000
110001101101=>001110010010=>101010011000
101001101101=>010110010010=>101011001000
100101101101=>011010010010=>101011010000
100011101101=>011100010010=>101001011000
110100011101=>001011100010=>100110001100
101100011101=>010011100010=>100101001100
110010011101=>001101100010=>100110010100
101010011101=>010101100010=>100111000100
100110011101=>011001100010=>100101010100
110001011101=>001110100010=>100110011000
101001011101=>010110100010=>100111001000
100101011101=>011010100010=>100111010000
100011011101=>011100100010=>100101011000
110000111101=>001111000010=>100010011100
101000111101=>010111000010=>100011001100
100100111101=>011011000010=>100011010100
100010111101=>011101000010=>100011011000
100001111101=>011110000010=>100001011100
110101010011=>001010101100=>011110000010
101101010011=>010010101100=>011101000010
110011010011=>001100101100=>011010010010
101011010011=>010100101100=>011011000010
100111010011=>011000101100=>011001010010
110100110011=>001011001100=>010110001010
101100110011=>010011001100=>010101001010
110010110011=>001101001100=>010110010010
101010110011=>010101001100=>010111000010
100110110011=>011001001100=>010101010010
110001110011=>001110001100=>010010011010
101001110011=>010110001100=>010011001010
100101110011=>011010001100=>010011010010
100011110011=>011100001100=>010001011010
110101001011=>001010110100=>011110000100
101101001011=>010010110100=>011101000100
110011001011=>001100110100=>011010010100
101011001011=>010100110100=>011011000100
100111001011=>011000110100=>011001010100
110100101011=>001011010100=>011110001000
101100101011=>010011010100=>011101001000
110010101011=>001101010100=>011110010000
101010101011=>010101010100=>011111000000
100110101011=>011001010100=>011101010000
110001101011=>001110010100=>011010011000
101001101011=>010110010100=>011011001000
100101101011=>011010010100=>011011010000
100011101011=>011100010100=>011001011000
110100011011=>001011100100=>010110001100
101100011011=>010011100100=>010101001100
110010011011=>001101100100=>010110010100
101010011011=>010101100100=>010111000100
100110011011=>011001100100=>010101010100
110001011011=>001110100100=>010110011000
101001011011=>010110100100=>010111001000
100101011011=>011010100100=>010111010000
100011011011=>011100100100=>010101011000
110000111011=>001111000100=>010010011100
101000111011=>010111000100=>010011001100
100100111011=>011011000100=>010011010100
100010111011=>011101000100=>010011011000
100001111011=>011110000100=>010001011100
110101000111=>001010111000=>001110000110
101101000111=>010010111000=>001101000110
110011000111=>001100111000=>001010010110
101011000111=>010100111000=>001011000110
100111000111=>011000111000=>001001010110
110100100111=>001011011000=>001110001010
101100100111=>010011011000=>001101001010
110010100111=>001101011000=>001110010010
101010100111=>010101011000=>001111000010
100110100111=>011001011000=>001101010010
110001100111=>001110011000=>001010011010
101001100111=>010110011000=>001011001010
100101100111=>011010011000=>001011010010
100011100111=>011100011000=>001001011010
110100010111=>001011101000=>001110001100
101100010111=>010011101000=>001101001100
110010010111=>001101101000=>001110010100
101010010111=>010101101000=>001111000100
100110010111=>011001101000=>001101010100
110001010111=>001110101000=>001110011000
101001010111=>010110101000=>001111001000
100101010111=>011010101000=>001111010000
100011010111=>011100101000=>001101011000
110000110111=>001111001000=>001010011100
101000110111=>010111001000=>001011001100
100100110111=>011011001000=>001011010100
100010110111=>011101001000=>001011011000
100001110111=>011110001000=>001001011100
110100001111=>001011110000=>000110001110
101100001111=>010011110000=>000101001110
110010001111=>001101110000=>000110010110
101010001111=>010101110000=>000111000110
100110001111=>011001110000=>000101010110
110001001111=>001110110000=>000110011010
101001001111=>010110110000=>000111001010
100101001111=>011010110000=>000111010010
100011001111=>011100110000=>000101011010
110000101111=>001111010000=>000110011100
101000101111=>010111010000=>000111001100
100100101111=>011011010000=>000111010100
100010101111=>011101010000=>000111011000
100001101111=>011110010000=>000101011100
110000011111=>001111100000=>000010011110
101000011111=>010111100000=>000011001110
100100011111=>011011100000=>000011010110
100010011111=>011101100000=>000011011010
100001011111=>011110100000=>000011011100
100000111111=>011111000000=>000001011110
0011111111=>1100000000=>0000000110
0000010111=>1111101000=>0011111100
00111111111=>11000000000=>00000000110
010100111100=>101011000011=>000111001011
010010111100=>101101000011=>000111010011
0011111001=>1100000110=>1000011010
0000110011=>1111001100=>0101111010
0000100111=>1111011000=>0011111010
0110100111=>1001011000=>0011010010
0110101101=>1001010010=>1011010000
0110110011=>1001001100=>0101010010
0100111011=>1011000100=>0100110100
0101010111=>1010101000=>0011110000
0001010101=>1110101010=>1111110000
0000110101=>1111001010=>1101111000
0111010101=>1000101010=>1110010000
0101110101=>1010001010=>1100110000
0011110101=>1100001010=>1100011000
0000011011=>1111100100=>0101111100
0001001011=>1110110100=>0111110100
0110001111=>1001110000=>0001010110
0110011011=>1001100100=>0101010100
111110110100=>000001001011=>101000000011
111011110100=>000100001011=>100010000011
100110111000=>011001000111=>001010100111
100101011100=>011010100011=>001110100011
101100100110=>010011011001=>011010010101
111000100110=>000111011001=>011000110101
0110101011=>1001010100=>0111010000
11110010000=>00001101111=>10000101111
100101101111=>011010010000=>000101101000
101101110011=>010010001100=>010010100010
100101111011=>011010000100=>010001101000
0101110011=>1010001100=>0100110010
0110010111=>1001101000=>0011010100
0100110111=>1011001000=>0010110100
0101100111=>1010011000=>0010110010
0101001111=>1010110000=>0001110010
101101001111=>010010110000=>000110100010
0110110101=>1001001010=>1101010000
0101011011=>1010100100=>0101110000
0111010011=>1000101100=>0110010010
0111000111=>1000111000=>0010010110
011010010000=>100101101111=>110100101111
010010110000=>101101001111=>011101001111
011010000100=>100101111011=>110100111011
010010001100=>101101110011=>011101011011
101010001000=>010101110111=>111000110111
100010101000=>011101010111=>111011000111
100001011000=>011110100111=>011011100111
100101001000=>011010110111=>111010010111
111011101010=>000100010101=>110010000001
111011010110=>000100101001=>011010000001
111010101110=>000101010001=>001110000001
111001011110=>000110100001=>000110001001
011011011110=>100100100001=>000101010001
010001011000=>101110100111=>011101100111
010100011000=>101011100111=>011100110111
010001010000=>101110101111=>111011001111
010010010000=>101101101111=>111010101111
010100010000=>101011101111=>111001101111
111110010110=>000001101001=>011000001001
111001110110=>000110001001=>010010001001
110000101100=>001111010011=>011001110011
110000100110=>001111011001=>011001110101
110000110010=>001111001101=>101001110101
110000010110=>001111101001=>011001111001
110000011010=>001111100101=>101001111001
111000001010=>000111110101=>110001111001
00100000000=>11011111111=>11011111111
11000000000=>00111111111=>00111111111
11111111100=>00000000011=>00000000011
111000001100=>000111110011=>010001111011
0011010001=>1100101110=>1101100110
0001000111=>1110111000=>0011110110
0001001101=>1110110010=>1011110100
0001010011=>1110101100=>0111110010
0000101011=>1111010100=>0111111000
0110011101=>1001100010=>1001010100
0111001101=>1000110010=>1010010100
100011001100=>011100110011=>010101101011
100010111000=>011101000111=>001101100111
0100111101=>1011000010=>1000110100
00111100001=>11000011110=>10001101110
100010101100=>011101010011=>011101100011
100010110010=>011101001101=>101101100101
100011001010=>011100110101=>110101101001
100011100010=>011100011101=>100101101101
100011110000=>011100001111=>000101101111
11111001000=>00000110111=>10000010111
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.
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