Identifier
Mp00104:
Binary words
—reverse⟶
Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Images
=>
0=>0=>0=>0
1=>1=>1=>1
00=>00=>00=>00
01=>10=>10=>01
10=>01=>01=>10
11=>11=>11=>11
000=>000=>000=>000
001=>100=>010=>100
010=>010=>100=>001
011=>110=>110=>101
100=>001=>001=>010
101=>101=>101=>011
110=>011=>011=>110
111=>111=>111=>111
0000=>0000=>0000=>0000
0001=>1000=>0010=>0100
0010=>0100=>0100=>1000
0011=>1100=>0110=>1100
0100=>0010=>1000=>0001
0101=>1010=>1100=>1001
0110=>0110=>1010=>0101
0111=>1110=>1110=>1101
1000=>0001=>0001=>0010
1001=>1001=>0101=>1010
1010=>0101=>1001=>0011
1011=>1101=>1101=>1011
1100=>0011=>0011=>0110
1101=>1011=>1011=>0111
1110=>0111=>0111=>1110
1111=>1111=>1111=>1111
00000=>00000=>00000=>00000
00001=>10000=>00010=>00100
00010=>01000=>00100=>01000
00011=>11000=>00110=>01100
00100=>00100=>01000=>10000
00101=>10100=>01100=>11000
00110=>01100=>01010=>10100
00111=>11100=>01110=>11100
01000=>00010=>10000=>00001
01001=>10010=>10100=>01001
01010=>01010=>11000=>10001
01011=>11010=>11100=>11001
01100=>00110=>10010=>00101
01101=>10110=>11010=>10101
01110=>01110=>10110=>01101
01111=>11110=>11110=>11101
10000=>00001=>00001=>00010
10001=>10001=>00101=>01010
10010=>01001=>01001=>10010
10011=>11001=>01101=>11010
10100=>00101=>10001=>00011
10101=>10101=>11001=>10011
10110=>01101=>10101=>01011
10111=>11101=>11101=>11011
11000=>00011=>00011=>00110
11001=>10011=>01011=>10110
11010=>01011=>10011=>00111
11011=>11011=>11011=>10111
11100=>00111=>00111=>01110
11101=>10111=>10111=>01111
11110=>01111=>01111=>11110
11111=>11111=>11111=>11111
000000=>000000=>000000=>000000
000001=>100000=>000010=>000100
000010=>010000=>000100=>001000
000011=>110000=>000110=>001100
000100=>001000=>001000=>010000
000101=>101000=>001100=>011000
000110=>011000=>001010=>010100
000111=>111000=>001110=>011100
001000=>000100=>010000=>100000
001001=>100100=>010100=>101000
001010=>010100=>011000=>110000
001011=>110100=>011100=>111000
001100=>001100=>010010=>100100
001101=>101100=>011010=>110100
001110=>011100=>010110=>101100
001111=>111100=>011110=>111100
010000=>000010=>100000=>000001
010001=>100010=>100100=>001001
010010=>010010=>101000=>010001
010011=>110010=>101100=>011001
010100=>001010=>110000=>100001
010101=>101010=>111000=>110001
010110=>011010=>110100=>101001
010111=>111010=>111100=>111001
011000=>000110=>100010=>000101
011001=>100110=>101010=>010101
011010=>010110=>110010=>100101
011011=>110110=>111010=>110101
011100=>001110=>100110=>001101
011101=>101110=>110110=>101101
011110=>011110=>101110=>011101
011111=>111110=>111110=>111101
100000=>000001=>000001=>000010
100001=>100001=>000101=>001010
100010=>010001=>001001=>010010
100011=>110001=>001101=>011010
100100=>001001=>010001=>100010
100101=>101001=>011001=>110010
100110=>011001=>010101=>101010
100111=>111001=>011101=>111010
101000=>000101=>100001=>000011
101001=>100101=>101001=>010011
101010=>010101=>110001=>100011
101011=>110101=>111001=>110011
101100=>001101=>100101=>001011
101101=>101101=>110101=>101011
101110=>011101=>101101=>011011
101111=>111101=>111101=>111011
110000=>000011=>000011=>000110
110001=>100011=>001011=>010110
110010=>010011=>010011=>100110
110011=>110011=>011011=>110110
110100=>001011=>100011=>000111
110101=>101011=>110011=>100111
110110=>011011=>101011=>010111
110111=>111011=>111011=>110111
111000=>000111=>000111=>001110
111001=>100111=>010111=>101110
111010=>010111=>100111=>001111
111011=>110111=>110111=>101111
111100=>001111=>001111=>011110
111101=>101111=>101111=>011111
111110=>011111=>011111=>111110
111111=>111111=>111111=>111111
0000000=>0000000=>0000000=>0000000
0000001=>1000000=>0000010=>0000100
0000010=>0100000=>0000100=>0001000
0000011=>1100000=>0000110=>0001100
0000100=>0010000=>0001000=>0010000
0000101=>1010000=>0001100=>0011000
0000110=>0110000=>0001010=>0010100
0000111=>1110000=>0001110=>0011100
0001000=>0001000=>0010000=>0100000
0001001=>1001000=>0010100=>0101000
0001010=>0101000=>0011000=>0110000
0001011=>1101000=>0011100=>0111000
0001100=>0011000=>0010010=>0100100
0001101=>1011000=>0011010=>0110100
0001110=>0111000=>0010110=>0101100
0001111=>1111000=>0011110=>0111100
0010000=>0000100=>0100000=>1000000
0010001=>1000100=>0100100=>1001000
0010010=>0100100=>0101000=>1010000
0010011=>1100100=>0101100=>1011000
0010100=>0010100=>0110000=>1100000
0010101=>1010100=>0111000=>1110000
0010110=>0110100=>0110100=>1101000
0010111=>1110100=>0111100=>1111000
0011000=>0001100=>0100010=>1000100
0011001=>1001100=>0101010=>1010100
0011010=>0101100=>0110010=>1100100
0011011=>1101100=>0111010=>1110100
0011100=>0011100=>0100110=>1001100
0011101=>1011100=>0110110=>1101100
0011110=>0111100=>0101110=>1011100
0011111=>1111100=>0111110=>1111100
0100000=>0000010=>1000000=>0000001
0100001=>1000010=>1000100=>0001001
0100010=>0100010=>1001000=>0010001
0100011=>1100010=>1001100=>0011001
0100100=>0010010=>1010000=>0100001
0100101=>1010010=>1011000=>0110001
0100110=>0110010=>1010100=>0101001
0100111=>1110010=>1011100=>0111001
0101000=>0001010=>1100000=>1000001
0101001=>1001010=>1101000=>1010001
0101010=>0101010=>1110000=>1100001
0101011=>1101010=>1111000=>1110001
0101100=>0011010=>1100100=>1001001
0101101=>1011010=>1110100=>1101001
0101110=>0111010=>1101100=>1011001
0101111=>1111010=>1111100=>1111001
0110000=>0000110=>1000010=>0000101
0110001=>1000110=>1001010=>0010101
0110010=>0100110=>1010010=>0100101
0110011=>1100110=>1011010=>0110101
0110100=>0010110=>1100010=>1000101
0110101=>1010110=>1110010=>1100101
0110110=>0110110=>1101010=>1010101
0110111=>1110110=>1111010=>1110101
0111000=>0001110=>1000110=>0001101
0111001=>1001110=>1010110=>0101101
0111010=>0101110=>1100110=>1001101
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0111100=>0011110=>1001110=>0011101
0111101=>1011110=>1101110=>1011101
0111110=>0111110=>1011110=>0111101
0111111=>1111110=>1111110=>1111101
1000000=>0000001=>0000001=>0000010
1000001=>1000001=>0000101=>0001010
1000010=>0100001=>0001001=>0010010
1000011=>1100001=>0001101=>0011010
1000100=>0010001=>0010001=>0100010
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1000110=>0110001=>0010101=>0101010
1000111=>1110001=>0011101=>0111010
1001000=>0001001=>0100001=>1000010
1001001=>1001001=>0101001=>1010010
1001010=>0101001=>0110001=>1100010
1001011=>1101001=>0111001=>1110010
1001100=>0011001=>0100101=>1001010
1001101=>1011001=>0110101=>1101010
1001110=>0111001=>0101101=>1011010
1001111=>1111001=>0111101=>1111010
1010000=>0000101=>1000001=>0000011
1010001=>1000101=>1001001=>0010011
1010010=>0100101=>1010001=>0100011
1010011=>1100101=>1011001=>0110011
1010100=>0010101=>1100001=>1000011
1010101=>1010101=>1110001=>1100011
1010110=>0110101=>1101001=>1010011
1010111=>1110101=>1111001=>1110011
1011000=>0001101=>1000101=>0001011
1011001=>1001101=>1010101=>0101011
1011010=>0101101=>1100101=>1001011
1011011=>1101101=>1110101=>1101011
1011100=>0011101=>1001101=>0011011
1011101=>1011101=>1101101=>1011011
1011110=>0111101=>1011101=>0111011
1011111=>1111101=>1111101=>1111011
1100000=>0000011=>0000011=>0000110
1100001=>1000011=>0001011=>0010110
1100010=>0100011=>0010011=>0100110
1100011=>1100011=>0011011=>0110110
1100100=>0010011=>0100011=>1000110
1100101=>1010011=>0110011=>1100110
1100110=>0110011=>0101011=>1010110
1100111=>1110011=>0111011=>1110110
1101000=>0001011=>1000011=>0000111
1101001=>1001011=>1010011=>0100111
1101010=>0101011=>1100011=>1000111
1101011=>1101011=>1110011=>1100111
1101100=>0011011=>1001011=>0010111
1101101=>1011011=>1101011=>1010111
1101110=>0111011=>1011011=>0110111
1101111=>1111011=>1111011=>1110111
1110000=>0000111=>0000111=>0001110
1110001=>1000111=>0010111=>0101110
1110010=>0100111=>0100111=>1001110
1110011=>1100111=>0110111=>1101110
1110100=>0010111=>1000111=>0001111
1110101=>1010111=>1100111=>1001111
1110110=>0110111=>1010111=>0101111
1110111=>1110111=>1110111=>1101111
1111000=>0001111=>0001111=>0011110
1111001=>1001111=>0101111=>1011110
1111010=>0101111=>1001111=>0011111
1111011=>1101111=>1101111=>1011111
1111100=>0011111=>0011111=>0111110
1111101=>1011111=>1011111=>0111111
1111110=>0111111=>0111111=>1111110
1111111=>1111111=>1111111=>1111111
00000000=>00000000=>00000000=>00000000
00000001=>10000000=>00000010=>00000100
00000010=>01000000=>00000100=>00001000
00000011=>11000000=>00000110=>00001100
00000100=>00100000=>00001000=>00010000
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00000110=>01100000=>00001010=>00010100
00000111=>11100000=>00001110=>00011100
00001000=>00010000=>00010000=>00100000
00001001=>10010000=>00010100=>00101000
00001010=>01010000=>00011000=>00110000
00001011=>11010000=>00011100=>00111000
00001100=>00110000=>00010010=>00100100
00001101=>10110000=>00011010=>00110100
00001110=>01110000=>00010110=>00101100
00001111=>11110000=>00011110=>00111100
00010000=>00001000=>00100000=>01000000
00010001=>10001000=>00100100=>01001000
00010010=>01001000=>00101000=>01010000
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00010100=>00101000=>00110000=>01100000
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00010110=>01101000=>00110100=>01101000
00010111=>11101000=>00111100=>01111000
00011000=>00011000=>00100010=>01000100
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00011010=>01011000=>00110010=>01100100
00011011=>11011000=>00111010=>01110100
00011100=>00111000=>00100110=>01001100
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00011110=>01111000=>00101110=>01011100
00011111=>11111000=>00111110=>01111100
00100000=>00000100=>01000000=>10000000
00100001=>10000100=>01000100=>10001000
00100010=>01000100=>01001000=>10010000
00100011=>11000100=>01001100=>10011000
00100100=>00100100=>01010000=>10100000
00100101=>10100100=>01011000=>10110000
00100110=>01100100=>01010100=>10101000
00100111=>11100100=>01011100=>10111000
00101000=>00010100=>01100000=>11000000
00101001=>10010100=>01101000=>11010000
00101010=>01010100=>01110000=>11100000
00101011=>11010100=>01111000=>11110000
00101100=>00110100=>01100100=>11001000
00101101=>10110100=>01110100=>11101000
00101110=>01110100=>01101100=>11011000
00101111=>11110100=>01111100=>11111000
00110000=>00001100=>01000010=>10000100
00110001=>10001100=>01001010=>10010100
00110010=>01001100=>01010010=>10100100
00110011=>11001100=>01011010=>10110100
00110100=>00101100=>01100010=>11000100
00110101=>10101100=>01110010=>11100100
00110110=>01101100=>01101010=>11010100
00110111=>11101100=>01111010=>11110100
00111000=>00011100=>01000110=>10001100
00111001=>10011100=>01010110=>10101100
00111010=>01011100=>01100110=>11001100
00111011=>11011100=>01110110=>11101100
00111100=>00111100=>01001110=>10011100
00111101=>10111100=>01101110=>11011100
00111110=>01111100=>01011110=>10111100
00111111=>11111100=>01111110=>11111100
01000000=>00000010=>10000000=>00000001
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01000010=>01000010=>10001000=>00010001
01000011=>11000010=>10001100=>00011001
01000100=>00100010=>10010000=>00100001
01000101=>10100010=>10011000=>00110001
01000110=>01100010=>10010100=>00101001
01000111=>11100010=>10011100=>00111001
01001000=>00010010=>10100000=>01000001
01001001=>10010010=>10101000=>01010001
01001010=>01010010=>10110000=>01100001
01001011=>11010010=>10111000=>01110001
01001100=>00110010=>10100100=>01001001
01001101=>10110010=>10110100=>01101001
01001110=>01110010=>10101100=>01011001
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01010001=>10001010=>11001000=>10010001
01010010=>01001010=>11010000=>10100001
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01010100=>00101010=>11100000=>11000001
01010101=>10101010=>11110000=>11100001
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01010111=>11101010=>11111000=>11110001
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01110111=>11101110=>11110110=>11101101
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01111011=>11011110=>11101110=>11011101
01111100=>00111110=>10011110=>00111101
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01111110=>01111110=>10111110=>01111101
01111111=>11111110=>11111110=>11111101
10000000=>00000001=>00000001=>00000010
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10001111=>11110001=>00111101=>01111010
10010000=>00001001=>01000001=>10000010
10010001=>10001001=>01001001=>10010010
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10010110=>01101001=>01101001=>11010010
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11101000=>00010111=>10000111=>00001111
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11101110=>01110111=>10110111=>01101111
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11110000=>00001111=>00001111=>00011110
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11110010=>01001111=>01001111=>10011110
11110011=>11001111=>01101111=>11011110
11110100=>00101111=>10001111=>00011111
11110101=>10101111=>11001111=>10011111
11110110=>01101111=>10101111=>01011111
11110111=>11101111=>11101111=>11011111
11111000=>00011111=>00011111=>00111110
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11111010=>01011111=>10011111=>00111111
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11111100=>00111111=>00111111=>01111110
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11111110=>01111111=>01111111=>11111110
11111111=>11111111=>11111111=>11111111
000000000=>000000000=>000000000=>000000000
000000001=>100000000=>000000010=>000000100
000000010=>010000000=>000000100=>000001000
000000011=>110000000=>000000110=>000001100
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000100000=>000001000=>001000000=>010000000
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000100010=>010001000=>001001000=>010010000
000100011=>110001000=>001001100=>010011000
000100100=>001001000=>001010000=>010100000
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000100110=>011001000=>001010100=>010101000
000100111=>111001000=>001011100=>010111000
000101000=>000101000=>001100000=>011000000
000101001=>100101000=>001101000=>011010000
000101010=>010101000=>001110000=>011100000
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1100111000=>0001110011=>0100011011=>1000110110
1101010010=>0100101011=>1101000011=>1010000111
1101010100=>0010101011=>1110000011=>1100000111
1110001010=>0101000111=>0011000111=>0110001110
1110001100=>0011000111=>0010010111=>0100101110
1110010010=>0100100111=>0101000111=>1010001110
1110011000=>0001100111=>0100010111=>1000101110
1110101000=>0001010111=>1100000111=>1000001111
1111000010=>0100001111=>0001001111=>0010011110
1111000100=>0010001111=>0010001111=>0100011110
1111001000=>0001001111=>0100001111=>1000011110
1111100000=>0000011111=>0000011111=>0000111110
101010101010=>010101010101=>111110000001=>111100000011
101010101100=>001101010101=>111100100001=>111001000011
101010110010=>010011010101=>111010010001=>110100100011
101010110100=>001011010101=>111100010001=>111000100011
101010111000=>000111010101=>111000110001=>110001100011
101011101000=>000101110101=>111000011001=>110000110011
101100101010=>010101001101=>101110000101=>011100001011
101100101100=>001101001101=>101100100101=>011001001011
101100110010=>010011001101=>101010010101=>010100101011
101100111000=>000111001101=>101000110101=>010001101011
101101010010=>010010101101=>111010000101=>110100001011
101101011000=>000110101101=>111000100101=>110001001011
101110001010=>010100011101=>100110001101=>001100011011
101110010100=>001010011101=>101100001101=>011000011011
101110101000=>000101011101=>111000001101=>110000011011
101111000010=>010000111101=>100010011101=>000100111011
101111001000=>000100111101=>101000011101=>010000111011
101111100000=>000001111101=>100000111101=>000001111011
110010101010=>010101010011=>011110000011=>111100000110
110010110100=>001011010011=>011100010011=>111000100110
110011001100=>001100110011=>010100101011=>101001010110
110011010010=>010010110011=>011010001011=>110100010110
110011011000=>000110110011=>011000101011=>110001010110
110011100010=>010001110011=>010010011011=>100100110110
110011100100=>001001110011=>010100011011=>101000110110
110011110000=>000011110011=>010000111011=>100001110110
110100101100=>001101001011=>101100100011=>011001000111
110100110100=>001011001011=>101100010011=>011000100111
110100111000=>000111001011=>101000110011=>010001100111
110101001010=>010100101011=>110110000011=>101100000111
110101010010=>010010101011=>111010000011=>110100000111
110101010100=>001010101011=>111100000011=>111000000111
110111000100=>001000111011=>100100011011=>001000110111
110111001000=>000100111011=>101000011011=>010000110111
111000101100=>001101000111=>001100100111=>011001001110
111000110010=>010011000111=>001010010111=>010100101110
111000110100=>001011000111=>001100010111=>011000101110
111000111000=>000111000111=>001000110111=>010001101110
111001001100=>001100100111=>010100100111=>101001001110
111001010100=>001010100111=>011100000111=>111000001110
111001100010=>010001100111=>010010010111=>100100101110
111001100100=>001001100111=>010100010111=>101000101110
111001101000=>000101100111=>011000010111=>110000101110
111001110000=>000011100111=>010000110111=>100001101110
111010001010=>010100010111=>100110000111=>001100001111
111010001100=>001100010111=>100100100111=>001001001111
111010010010=>010010010111=>101010000111=>010100001111
111010010100=>001010010111=>101100000111=>011000001111
111010011000=>000110010111=>101000100111=>010001001111
111010100100=>001001010111=>110100000111=>101000001111
111010101000=>000101010111=>111000000111=>110000001111
111011000010=>010000110111=>100010010111=>000100101111
111011000100=>001000110111=>100100010111=>001000101111
111011001000=>000100110111=>101000010111=>010000101111
111011100000=>000001110111=>100000110111=>000001101111
111100001010=>010100001111=>000110001111=>001100011110
111100001100=>001100001111=>000100101111=>001001011110
111100010010=>010010001111=>001010001111=>010100011110
111100010100=>001010001111=>001100001111=>011000011110
111100011000=>000110001111=>001000101111=>010001011110
111100100010=>010001001111=>010010001111=>100100011110
111100100100=>001001001111=>010100001111=>101000011110
111100110000=>000011001111=>010000101111=>100001011110
111101010000=>000010101111=>110000001111=>100000011111
111110000010=>010000011111=>000010011111=>000100111110
111110000100=>001000011111=>000100011111=>001000111110
111110001000=>000100011111=>001000011111=>010000111110
111110010000=>000010011111=>010000011111=>100000111110
111110100000=>000001011111=>100000011111=>000000111111
111111000000=>000000111111=>000000111111=>000001111110
1111111111=>1111111111=>1111111111=>1111111111
1111111110=>0111111111=>0111111111=>1111111110
1111111011=>1101111111=>1101111111=>1011111111
1111110111=>1110111111=>1110111111=>1101111111
1111110000=>0000111111=>0000111111=>0001111110
1111101101=>1011011111=>1101011111=>1010111111
1111101011=>1101011111=>1110011111=>1100111111
1111000011=>1100001111=>0001101111=>0011011110
1110111000=>0001110111=>1000110111=>0001101111
1110110010=>0100110111=>1010010111=>0100101111
1110100101=>1010010111=>1011000111=>0110001111
1110001101=>1011000111=>0011010111=>0110101110
1110000111=>1110000111=>0001110111=>0011101110
1101010110=>0110101011=>1110100011=>1101000111
1100111010=>0101110011=>0110011011=>1100110110
1100110110=>0110110011=>0110101011=>1101010110
1100101110=>0111010011=>0110110011=>1101100110
1100101011=>1101010011=>0111100011=>1111000110
1100100111=>1110010011=>0101110011=>1011100110
1100100110=>0110010011=>0101010011=>1010100110
1100100010=>0100010011=>0100100011=>1001000110
1100011010=>0101100011=>0011001011=>0110010110
1100010111=>1110100011=>0011110011=>0111100110
1100010110=>0110100011=>0011010011=>0110100110
1100001010=>0101000011=>0001100011=>0011000110
1100000000=>0000000011=>0000000011=>0000000110
1011111110=>0111111101=>1011111101=>0111111011
1011100101=>1010011101=>1011001101=>0110011011
1011011001=>1001101101=>1101010101=>1010101011
1011001101=>1011001101=>1011010101=>0110101011
1011001011=>1101001101=>1011100101=>0111001011
1011000001=>1000001101=>1000010101=>0000101011
1011000000=>0000001101=>1000000101=>0000001011
1010110101=>1010110101=>1111001001=>1110010011
1010110011=>1100110101=>1101101001=>1011010011
1010101101=>1011010101=>1111010001=>1110100011
1010101011=>1101010101=>1111100001=>1111000011
1010101000=>0001010101=>1110000001=>1100000011
1010100111=>1110010101=>1101110001=>1011100011
1010100110=>0110010101=>1101010001=>1010100011
1010011101=>1011100101=>1011011001=>0110110011
1010010111=>1110100101=>1011110001=>0111100011
1010010001=>1000100101=>1010010001=>0100100011
1010001111=>1111000101=>1001111001=>0011110011
1010001010=>0101000101=>1001100001=>0011000011
1010000101=>1010000101=>1000110001=>0001100011
1001111111=>1111111001=>0111111101=>1111111010
1001110010=>0100111001=>0101001101=>1010011010
1001101110=>0111011001=>0110110101=>1101101010
1001101101=>1011011001=>0111010101=>1110101010
1001101011=>1101011001=>0111100101=>1111001010
1001100110=>0110011001=>0101010101=>1010101010
1001100001=>1000011001=>0100010101=>1000101010
1001011110=>0111101001=>0110111001=>1101110010
1001011011=>1101101001=>0111101001=>1111010010
1001011000=>0001101001=>0110001001=>1100010010
1001010111=>1110101001=>0111110001=>1111100010
1001010010=>0100101001=>0110100001=>1101000010
1001001111=>1111001001=>0101111001=>1011110010
1000111010=>0101110001=>0011001101=>0110011010
1000110111=>1110110001=>0011110101=>0111101010
1000110110=>0110110001=>0011010101=>0110101010
1000101111=>1111010001=>0011111001=>0111110010
1000100000=>0000010001=>0010000001=>0100000010
1000011111=>1111100001=>0001111101=>0011111010
1000011110=>0111100001=>0001011101=>0010111010
1000011001=>1001100001=>0001010101=>0010101010
1000010110=>0110100001=>0001101001=>0011010010
1000001101=>1011000001=>0000110101=>0001101010
1000000100=>0010000001=>0000010001=>0000100010
1000000001=>1000000001=>0000000101=>0000001010
1000000000=>0000000001=>0000000001=>0000000010
10000000000=>00000000001=>00000000001=>00000000010
11111111110=>01111111111=>01111111111=>11111111110
100000010110=>011010000001=>000001101001=>000011010010
100001101110=>011101100001=>000110110101=>001101101010
100001010010=>010010100001=>000110100001=>001101000010
110000101110=>011101000011=>000110110011=>001101100110
100110001110=>011100011001=>010010110101=>100101101010
100101010110=>011010101001=>011110100001=>111101000010
0111111111=>1111111110=>1111111110=>1111111101
0111111101=>1011111110=>1101111110=>1011111101
0111111001=>1001111110=>1010111110=>0101111101
0111110001=>1000111110=>1001011110=>0010111101
0111100001=>1000011110=>1000101110=>0001011101
0111000001=>1000001110=>1000010110=>0000101101
0110000001=>1000000110=>1000001010=>0000010101
0100000001=>1000000010=>1000000100=>0000001001
0000000001=>1000000000=>0000000010=>0000000100
01111111111=>11111111110=>11111111110=>11111111101
0111111011=>1101111110=>1110111110=>1101111101
0010000001=>1000000100=>0100000100=>1000001000
00000000001=>10000000000=>00000000010=>00000000100
0101010101=>1010101010=>1111100000=>1111000001
0101010011=>1100101010=>1110110000=>1101100001
0101001101=>1011001010=>1101101000=>1011010001
0101001011=>1101001010=>1101110000=>1011100001
0101000111=>1110001010=>1100111000=>1001110001
0100110101=>1010110010=>1011100100=>0111001001
0100110011=>1100110010=>1010110100=>0101101001
0100101101=>1011010010=>1011101000=>0111010001
0100101011=>1101010010=>1011110000=>0111100001
0100100111=>1110010010=>1010111000=>0101110001
0010110101=>1010110100=>0111100100=>1111001000
0010101101=>1011010100=>0111101000=>1111010000
0010101011=>1101010100=>0111110000=>1111100000
0001011011=>1101101000=>0011110100=>0111101000
0001010111=>1110101000=>0011111000=>0111110000
0000101111=>1111010000=>0001111100=>0011111000
0000011111=>1111100000=>0000111110=>0001111100
010101010101=>101010101010=>111111000000=>111110000001
010101001101=>101100101010=>111011010000=>110110100001
010101001011=>110100101010=>111011100000=>110111000001
010100110101=>101011001010=>110111001000=>101110010001
010100101101=>101101001010=>110111010000=>101110100001
010100101011=>110101001010=>110111100000=>101111000001
010100100111=>111001001010=>110101110000=>101011100001
010100011011=>110110001010=>110011101000=>100111010001
010100010111=>111010001010=>110011110000=>100111100001
010100001111=>111100001010=>110001111000=>100011110001
010011010101=>101010110010=>101111000100=>011110001001
010011010011=>110010110010=>101101100100=>011011001001
010011001101=>101100110010=>101011010100=>010110101001
010011001011=>110100110010=>101011100100=>010111001001
010010110101=>101011010010=>101111001000=>011110010001
010010101101=>101101010010=>101111010000=>011110100001
010010101011=>110101010010=>101111100000=>011111000001
010010011101=>101110010010=>101011011000=>010110110001
010010011011=>110110010010=>101011101000=>010111010001
010010010111=>111010010010=>101011110000=>010111100001
001011010101=>101010110100=>011111000100=>111110001000
001011001101=>101100110100=>011011010100=>110110101000
001010110101=>101011010100=>011111001000=>111110010000
001010101101=>101101010100=>011111010000=>111110100000
001010101011=>110101010100=>011111100000=>111111000000
001000111101=>101111000100=>010011011100=>100110111000
000101110101=>101011101000=>001111001100=>011110011000
000101101101=>101101101000=>001111010100=>011110101000
000101101011=>110101101000=>001111100100=>011111001000
000101011101=>101110101000=>001111011000=>011110110000
000101011011=>110110101000=>001111101000=>011111010000
000101010111=>111010101000=>001111110000=>011111100000
000010111101=>101111010000=>000111011100=>001110111000
000010110111=>111011010000=>000111110100=>001111101000
000010101111=>111101010000=>000111111000=>001111110000
000001011111=>111110100000=>000011111100=>000111111000
111111111111=>111111111111=>111111111111=>111111111111
111110011111=>111110011111=>011111011111=>111110111110
111110000001=>100000011111=>000001011111=>000010111110
111110110001=>100011011111=>100101011111=>001010111111
111110100101=>101001011111=>101100011111=>011000111111
111001111001=>100111100111=>010101110111=>101011101110
111001100001=>100001100111=>010001010111=>100010101110
111001101101=>101101100111=>011101010111=>111010101110
111000011001=>100110000111=>000101010111=>001010101110
111000000111=>111000000111=>000001110111=>000011101110
111000001101=>101100000111=>000011010111=>000110101110
111000110001=>100011000111=>001001010111=>010010101110
111000100101=>101001000111=>001011000111=>010110001110
111011110001=>100011110111=>100101110111=>001011101111
111011100101=>101001110111=>101100110111=>011001101111
111010010111=>111010010111=>101111000111=>011110001111
111010010001=>100010010111=>101001000111=>010010001111
111010011101=>101110010111=>101101100111=>011011001111
111010000101=>101000010111=>100011000111=>000110001111
100111100001=>100001111001=>010001011101=>100010111010
100110011001=>100110011001=>010101010101=>101010101010
100110000111=>111000011001=>010001110101=>100011101010
100110000001=>100000011001=>010000010101=>100000101010
100110001101=>101100011001=>010011010101=>100110101010
100110111101=>101111011001=>011101110101=>111011101010
100110100101=>101001011001=>011011000101=>110110001010
100001111001=>100111100001=>000101011101=>001010111010
100001100111=>111001100001=>000101110101=>001011101010
100001100001=>100001100001=>000100010101=>001000101010
100001101101=>101101100001=>000111010101=>001110101010
100000011111=>111110000001=>000001111101=>000011111010
100000011001=>100110000001=>000001010101=>000010101010
100000000001=>100000000001=>000000000101=>000000001010
100000110111=>111011000001=>000011110101=>000111101010
100000111101=>101111000001=>000011011101=>000110111010
100011011001=>100110110001=>001101010101=>011010101010
100011000111=>111000110001=>001001110101=>010011101010
100011001101=>101100110001=>001011010101=>010110101010
100011110001=>100011110001=>001001011101=>010010111010
100011100101=>101001110001=>001011001101=>010110011010
101100100101=>101001001101=>101011000101=>010110001011
101111100101=>101001111101=>101100111101=>011001111011
101110010111=>111010011101=>101111001101=>011110011011
101110010001=>100010011101=>101001001101=>010010011011
101110011101=>101110011101=>101101101101=>011011011011
101110000101=>101000011101=>100011001101=>000110011011
101001011111=>111110100101=>101111110001=>011111100011
101001000111=>111000100101=>101001110001=>010011100011
101001000001=>100000100101=>101000010001=>010000100011
101001001101=>101100100101=>101011010001=>010110100011
101001110111=>111011100101=>101111011001=>011110110011
101001110001=>100011100101=>101001011001=>010010110011
101001111101=>101111100101=>101101111001=>011011110011
101000010111=>111010000101=>100011110001=>000111100011
101000010001=>100010000101=>100010010001=>000100100011
101000011101=>101110000101=>100011011001=>000110110011
101000000101=>101000000101=>100000110001=>000001100011
101010010101=>101010010101=>110111000001=>101110000011
0000000000=>0000000000=>0000000000=>0000000000
0111100000=>0000011110=>1000001110=>0000011101
0111111000=>0001111110=>1000111110=>0001111101
0111111110=>0111111110=>1011111110=>0111111101
000000000000=>000000000000=>000000000000=>000000000000
0000001010=>0101000000=>0000011000=>0000110000
01111111110=>01111111110=>10111111110=>01111111101
0110001100=>0011000110=>1001001010=>0010010101
001010101010=>010101010100=>011111000000=>111110000000
001010101100=>001101010100=>011110010000=>111100100000
001010110010=>010011010100=>011101001000=>111010010000
001010110100=>001011010100=>011110001000=>111100010000
001011001010=>010100110100=>011011000100=>110110001000
001011001100=>001100110100=>011010010100=>110100101000
001011010010=>010010110100=>011101000100=>111010001000
001011010100=>001010110100=>011110000100=>111100001000
001100101010=>010101001100=>010111000010=>101110000100
001100101100=>001101001100=>010110010010=>101100100100
001100110010=>010011001100=>010101001010=>101010010100
001100110100=>001011001100=>010110001010=>101100010100
001101001010=>010100101100=>011011000010=>110110000100
001101001100=>001100101100=>011010010010=>110100100100
001101010010=>010010101100=>011101000010=>111010000100
001101010100=>001010101100=>011110000010=>111100000100
0100000000=>0000000010=>1000000000=>0000000001
01000000000=>00000000010=>10000000000=>00000000001
0111110000=>0000111110=>1000011110=>0000111101
110010011001=>100110010011=>010101010011=>101010100110
111000010101=>101010000111=>000111000111=>001110001110
111000101001=>100101000111=>001101000111=>011010001110
111010001001=>100100010111=>100101000111=>001010001111
001001110100=>001011100100=>010110001100=>101100011000
000101110100=>001011101000=>001110001100=>011100011000
001001101100=>001101100100=>010110010100=>101100101000
000101101100=>001101101000=>001110010100=>011100101000
001010011100=>001110010100=>011010011000=>110100110000
001001011100=>001110100100=>010110011000=>101100110000
000101011100=>001110101000=>001110011000=>011100110000
001001011010=>010110100100=>010111001000=>101110010000
001011000110=>011000110100=>011001010100=>110010101000
001001100110=>011001100100=>010101010100=>101010101000
001010010110=>011010010100=>011011010000=>110110100000
001000110110=>011011000100=>010011010100=>100110101000
11111111111=>11111111111=>11111111111=>11111111111
101010010110=>011010010101=>110110100001=>101101000011
100001011101=>101110100001=>000111011001=>001110110010
110111000101=>101000111011=>100110011011=>001100110111
111011000101=>101000110111=>100110010111=>001100101111
111101001001=>100100101111=>101010001111=>010100011111
110000110101=>101011000011=>000111001011=>001110010110
110010001101=>101100010011=>010011010011=>100110100110
110000101101=>101101000011=>000111010011=>001110100110
001010110110=>011011010100=>011110101000=>111101010000
101010110011=>110011010101=>111011010001=>110110100011
101011001011=>110100110101=>110111001001=>101110010011
110010101011=>110101010011=>011111000011=>111110000110
101010101011=>110101010101=>111111000001=>111110000011
100110101011=>110101011001=>011111000101=>111110001010
100101101011=>110101101001=>011111001001=>111110010010
100011101011=>110101110001=>001111001101=>011110011010
101010011011=>110110010101=>110111010001=>101110100011
110001011011=>110110100011=>001111010011=>011110100110
100101011011=>110110101001=>011111010001=>111110100010
100011011011=>110110110001=>001111010101=>011110101010
100010111011=>110111010001=>001111011001=>011110110010
101011000111=>111000110101=>110011101001=>100111010011
101010100111=>111001010101=>111011100001=>110111000011
101010010111=>111010010101=>110111100001=>101111000011
110001010111=>111010100011=>001111100011=>011111000110
100101010111=>111010101001=>011111100001=>111111000010
100011010111=>111010110001=>001111100101=>011111001010
100010110111=>111011010001=>001111101001=>011111010010
101010001111=>111100010101=>110011110001=>100111100011
101001001111=>111100100101=>101011110001=>010111100011
110000101111=>111101000011=>000111110011=>001111100110
100010101111=>111101010001=>001111110001=>011111100010
100001101111=>111101100001=>000111110101=>001111101010
100001011111=>111110100001=>000111111001=>001111110010
100000111111=>111111000001=>000011111101=>000111111010
0000111111=>1111110000=>0001111110=>0011111100
0011111100=>0011111100=>0100111110=>1001111100
0010011001=>1001100100=>0101010100=>1010101000
0010100101=>1010010100=>0110110000=>1101100000
0001101111=>1111011000=>0011111010=>0111110100
0100101001=>1001010010=>1011010000=>0110100001
110010001110=>011100010011=>010010110011=>100101100110
110100010110=>011010001011=>100110100011=>001101000111
111101110010=>010011101111=>101001101111=>010011011111
111101001110=>011100101111=>101011001111=>010110011111
0100010101=>1010100010=>1001110000=>0011100001
0101010111=>1110101010=>1111110000=>1111100001
0001010101=>1010101000=>0011110000=>0111100000
0001110111=>1110111000=>0011110110=>0111101100
111000101011=>110101000111=>001111000111=>011110001110
111010001101=>101100010111=>100110100111=>001101001111
101011100011=>110001110101=>110011011001=>100110110011
100110111000=>000111011001=>011000110101=>110001101010
100110110010=>010011011001=>011010010101=>110100101010
111000100110=>011001000111=>001010100111=>010101001110
100001001001=>100100100001=>000101010001=>001010100010
0100011001=>1001100010=>1001010100=>0010101001
0100110001=>1000110010=>1010010100=>0100101001
101000101000=>000101000101=>100110000001=>001100000011
100001011000=>000110100001=>000110001001=>001100010010
100101001000=>000100101001=>011010000001=>110100000010
100100011000=>000110001001=>010010001001=>100100010010
110010100110=>011001010011=>011010100011=>110101000110
11000000000=>00000000011=>00000000011=>00000000110
101001111100=>001111100101=>101001111001=>010011110011
111111100000=>000001111111=>000001111111=>000011111110
Map
reverse
Description
Return the reversal of a binary word.
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
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.
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