Identifier
Mp00096:
Binary words
—Foata bijection⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00104: Binary words —reverse⟶ 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=>01=>10=>01
10=>10=>01=>10
11=>11=>11=>11
000=>000=>000=>000
001=>001=>100=>001
010=>100=>001=>010
011=>011=>110=>101
100=>010=>010=>100
101=>101=>101=>011
110=>110=>011=>110
111=>111=>111=>111
0000=>0000=>0000=>0000
0001=>0001=>1000=>0001
0010=>1000=>0001=>0010
0011=>0011=>1100=>1001
0100=>0100=>0010=>0100
0101=>1001=>1001=>0011
0110=>1010=>0101=>1010
0111=>0111=>1110=>1101
1000=>0010=>0100=>1000
1001=>0101=>1010=>0101
1010=>1100=>0011=>0110
1011=>1011=>1101=>1011
1100=>0110=>0110=>1100
1101=>1101=>1011=>0111
1110=>1110=>0111=>1110
1111=>1111=>1111=>1111
00000=>00000=>00000=>00000
00001=>00001=>10000=>00001
00010=>10000=>00001=>00010
00011=>00011=>11000=>10001
00100=>01000=>00010=>00100
00101=>10001=>10001=>00011
00110=>10010=>01001=>10010
00111=>00111=>11100=>11001
01000=>00100=>00100=>01000
01001=>01001=>10010=>00101
01010=>11000=>00011=>00110
01011=>10011=>11001=>10011
01100=>01010=>01010=>10100
01101=>10101=>10101=>01011
01110=>10110=>01101=>11010
01111=>01111=>11110=>11101
10000=>00010=>01000=>10000
10001=>00101=>10100=>01001
10010=>10100=>00101=>01010
10011=>01011=>11010=>10101
10100=>01100=>00110=>01100
10101=>11001=>10011=>00111
10110=>11010=>01011=>10110
10111=>10111=>11101=>11011
11000=>00110=>01100=>11000
11001=>01101=>10110=>01101
11010=>11100=>00111=>01110
11011=>11011=>11011=>10111
11100=>01110=>01110=>11100
11101=>11101=>10111=>01111
11110=>11110=>01111=>11110
11111=>11111=>11111=>11111
000000=>000000=>000000=>000000
000001=>000001=>100000=>000001
000010=>100000=>000001=>000010
000011=>000011=>110000=>100001
000100=>010000=>000010=>000100
000101=>100001=>100001=>000011
000110=>100010=>010001=>100010
000111=>000111=>111000=>110001
001000=>001000=>000100=>001000
001001=>010001=>100010=>000101
001010=>110000=>000011=>000110
001011=>100011=>110001=>100011
001100=>010010=>010010=>100100
001101=>100101=>101001=>010011
001110=>100110=>011001=>110010
001111=>001111=>111100=>111001
010000=>000100=>001000=>010000
010001=>001001=>100100=>001001
010010=>101000=>000101=>001010
010011=>010011=>110010=>100101
010100=>011000=>000110=>001100
010101=>110001=>100011=>000111
010110=>110010=>010011=>100110
010111=>100111=>111001=>110011
011000=>001010=>010100=>101000
011001=>010101=>101010=>010101
011010=>110100=>001011=>010110
011011=>101011=>110101=>101011
011100=>010110=>011010=>110100
011101=>101101=>101101=>011011
011110=>101110=>011101=>111010
011111=>011111=>111110=>111101
100000=>000010=>010000=>100000
100001=>000101=>101000=>010001
100010=>100100=>001001=>010010
100011=>001011=>110100=>101001
100100=>010100=>001010=>010100
100101=>101001=>100101=>001011
100110=>101010=>010101=>101010
100111=>010111=>111010=>110101
101000=>001100=>001100=>011000
101001=>011001=>100110=>001101
101010=>111000=>000111=>001110
101011=>110011=>110011=>100111
101100=>011010=>010110=>101100
101101=>110101=>101011=>010111
101110=>110110=>011011=>110110
101111=>101111=>111101=>111011
110000=>000110=>011000=>110000
110001=>001101=>101100=>011001
110010=>101100=>001101=>011010
110011=>011011=>110110=>101101
110100=>011100=>001110=>011100
110101=>111001=>100111=>001111
110110=>111010=>010111=>101110
110111=>110111=>111011=>110111
111000=>001110=>011100=>111000
111001=>011101=>101110=>011101
111010=>111100=>001111=>011110
111011=>111011=>110111=>101111
111100=>011110=>011110=>111100
111101=>111101=>101111=>011111
111110=>111110=>011111=>111110
111111=>111111=>111111=>111111
0000000=>0000000=>0000000=>0000000
0000001=>0000001=>1000000=>0000001
0000010=>1000000=>0000001=>0000010
0000011=>0000011=>1100000=>1000001
0000100=>0100000=>0000010=>0000100
0000101=>1000001=>1000001=>0000011
0000110=>1000010=>0100001=>1000010
0000111=>0000111=>1110000=>1100001
0001000=>0010000=>0000100=>0001000
0001001=>0100001=>1000010=>0000101
0001010=>1100000=>0000011=>0000110
0001011=>1000011=>1100001=>1000011
0001100=>0100010=>0100010=>1000100
0001101=>1000101=>1010001=>0100011
0001110=>1000110=>0110001=>1100010
0001111=>0001111=>1111000=>1110001
0010000=>0001000=>0001000=>0010000
0010001=>0010001=>1000100=>0001001
0010010=>1010000=>0000101=>0001010
0010011=>0100011=>1100010=>1000101
0010100=>0110000=>0000110=>0001100
0010101=>1100001=>1000011=>0000111
0010110=>1100010=>0100011=>1000110
0010111=>1000111=>1110001=>1100011
0011000=>0010010=>0100100=>1001000
0011001=>0100101=>1010010=>0100101
0011010=>1100100=>0010011=>0100110
0011011=>1001011=>1101001=>1010011
0011100=>0100110=>0110010=>1100100
0011101=>1001101=>1011001=>0110011
0011110=>1001110=>0111001=>1110010
0011111=>0011111=>1111100=>1111001
0100000=>0000100=>0010000=>0100000
0100001=>0001001=>1001000=>0010001
0100010=>1001000=>0001001=>0010010
0100011=>0010011=>1100100=>1001001
0100100=>0101000=>0001010=>0010100
0100101=>1010001=>1000101=>0001011
0100110=>1010010=>0100101=>1001010
0100111=>0100111=>1110010=>1100101
0101000=>0011000=>0001100=>0011000
0101001=>0110001=>1000110=>0001101
0101010=>1110000=>0000111=>0001110
0101011=>1100011=>1100011=>1000111
0101100=>0110010=>0100110=>1001100
0101101=>1100101=>1010011=>0100111
0101110=>1100110=>0110011=>1100110
0101111=>1001111=>1111001=>1110011
0110000=>0001010=>0101000=>1010000
0110001=>0010101=>1010100=>0101001
0110010=>1010100=>0010101=>0101010
0110011=>0101011=>1101010=>1010101
0110100=>0110100=>0010110=>0101100
0110101=>1101001=>1001011=>0010111
0110110=>1101010=>0101011=>1010110
0110111=>1010111=>1110101=>1101011
0111000=>0010110=>0110100=>1101000
0111001=>0101101=>1011010=>0110101
0111010=>1101100=>0011011=>0110110
0111011=>1011011=>1101101=>1011011
0111100=>0101110=>0111010=>1110100
0111101=>1011101=>1011101=>0111011
0111110=>1011110=>0111101=>1111010
0111111=>0111111=>1111110=>1111101
1000000=>0000010=>0100000=>1000000
1000001=>0000101=>1010000=>0100001
1000010=>1000100=>0010001=>0100010
1000011=>0001011=>1101000=>1010001
1000100=>0100100=>0010010=>0100100
1000101=>1001001=>1001001=>0010011
1000110=>1001010=>0101001=>1010010
1000111=>0010111=>1110100=>1101001
1001000=>0010100=>0010100=>0101000
1001001=>0101001=>1001010=>0010101
1001010=>1101000=>0001011=>0010110
1001011=>1010011=>1100101=>1001011
1001100=>0101010=>0101010=>1010100
1001101=>1010101=>1010101=>0101011
1001110=>1010110=>0110101=>1101010
1001111=>0101111=>1111010=>1110101
1010000=>0001100=>0011000=>0110000
1010001=>0011001=>1001100=>0011001
1010010=>1011000=>0001101=>0011010
1010011=>0110011=>1100110=>1001101
1010100=>0111000=>0001110=>0011100
1010101=>1110001=>1000111=>0001111
1010110=>1110010=>0100111=>1001110
1010111=>1100111=>1110011=>1100111
1011000=>0011010=>0101100=>1011000
1011001=>0110101=>1010110=>0101101
1011010=>1110100=>0010111=>0101110
1011011=>1101011=>1101011=>1010111
1011100=>0110110=>0110110=>1101100
1011101=>1101101=>1011011=>0110111
1011110=>1101110=>0111011=>1110110
1011111=>1011111=>1111101=>1111011
1100000=>0000110=>0110000=>1100000
1100001=>0001101=>1011000=>0110001
1100010=>1001100=>0011001=>0110010
1100011=>0011011=>1101100=>1011001
1100100=>0101100=>0011010=>0110100
1100101=>1011001=>1001101=>0011011
1100110=>1011010=>0101101=>1011010
1100111=>0110111=>1110110=>1101101
1101000=>0011100=>0011100=>0111000
1101001=>0111001=>1001110=>0011101
1101010=>1111000=>0001111=>0011110
1101011=>1110011=>1100111=>1001111
1101100=>0111010=>0101110=>1011100
1101101=>1110101=>1010111=>0101111
1101110=>1110110=>0110111=>1101110
1101111=>1101111=>1111011=>1110111
1110000=>0001110=>0111000=>1110000
1110001=>0011101=>1011100=>0111001
1110010=>1011100=>0011101=>0111010
1110011=>0111011=>1101110=>1011101
1110100=>0111100=>0011110=>0111100
1110101=>1111001=>1001111=>0011111
1110110=>1111010=>0101111=>1011110
1110111=>1110111=>1110111=>1101111
1111000=>0011110=>0111100=>1111000
1111001=>0111101=>1011110=>0111101
1111010=>1111100=>0011111=>0111110
1111011=>1111011=>1101111=>1011111
1111100=>0111110=>0111110=>1111100
1111101=>1111101=>1011111=>0111111
1111110=>1111110=>0111111=>1111110
1111111=>1111111=>1111111=>1111111
00000000=>00000000=>00000000=>00000000
00000001=>00000001=>10000000=>00000001
00000010=>10000000=>00000001=>00000010
00000011=>00000011=>11000000=>10000001
00000100=>01000000=>00000010=>00000100
00000101=>10000001=>10000001=>00000011
00000110=>10000010=>01000001=>10000010
00000111=>00000111=>11100000=>11000001
00001000=>00100000=>00000100=>00001000
00001001=>01000001=>10000010=>00000101
00001010=>11000000=>00000011=>00000110
00001011=>10000011=>11000001=>10000011
00001100=>01000010=>01000010=>10000100
00001101=>10000101=>10100001=>01000011
00001110=>10000110=>01100001=>11000010
00001111=>00001111=>11110000=>11100001
00010000=>00010000=>00001000=>00010000
00010001=>00100001=>10000100=>00001001
00010010=>10100000=>00000101=>00001010
00010011=>01000011=>11000010=>10000101
00010100=>01100000=>00000110=>00001100
00010101=>11000001=>10000011=>00000111
00010110=>11000010=>01000011=>10000110
00010111=>10000111=>11100001=>11000011
00011000=>00100010=>01000100=>10001000
00011001=>01000101=>10100010=>01000101
00011010=>11000100=>00100011=>01000110
00011011=>10001011=>11010001=>10100011
00011100=>01000110=>01100010=>11000100
00011101=>10001101=>10110001=>01100011
00011110=>10001110=>01110001=>11100010
00011111=>00011111=>11111000=>11110001
00100000=>00001000=>00010000=>00100000
00100001=>00010001=>10001000=>00010001
00100010=>10010000=>00001001=>00010010
00100011=>00100011=>11000100=>10001001
00100100=>01010000=>00001010=>00010100
00100101=>10100001=>10000101=>00001011
00100110=>10100010=>01000101=>10001010
00100111=>01000111=>11100010=>11000101
00101000=>00110000=>00001100=>00011000
00101001=>01100001=>10000110=>00001101
00101010=>11100000=>00000111=>00001110
00101011=>11000011=>11000011=>10000111
00101100=>01100010=>01000110=>10001100
00101101=>11000101=>10100011=>01000111
00101110=>11000110=>01100011=>11000110
00101111=>10001111=>11110001=>11100011
00110000=>00010010=>01001000=>10010000
00110001=>00100101=>10100100=>01001001
00110010=>10100100=>00100101=>01001010
00110011=>01001011=>11010010=>10100101
00110100=>01100100=>00100110=>01001100
00110101=>11001001=>10010011=>00100111
00110110=>11001010=>01010011=>10100110
00110111=>10010111=>11101001=>11010011
00111000=>00100110=>01100100=>11001000
00111001=>01001101=>10110010=>01100101
00111010=>11001100=>00110011=>01100110
00111011=>10011011=>11011001=>10110011
00111100=>01001110=>01110010=>11100100
00111101=>10011101=>10111001=>01110011
00111110=>10011110=>01111001=>11110010
00111111=>00111111=>11111100=>11111001
01000000=>00000100=>00100000=>01000000
01000001=>00001001=>10010000=>00100001
01000010=>10001000=>00010001=>00100010
01000011=>00010011=>11001000=>10010001
01000100=>01001000=>00010010=>00100100
01000101=>10010001=>10001001=>00010011
01000110=>10010010=>01001001=>10010010
01000111=>00100111=>11100100=>11001001
01001000=>00101000=>00010100=>00101000
01001001=>01010001=>10001010=>00010101
01001010=>11010000=>00001011=>00010110
01001011=>10100011=>11000101=>10001011
01001100=>01010010=>01001010=>10010100
01001101=>10100101=>10100101=>01001011
01001110=>10100110=>01100101=>11001010
01001111=>01001111=>11110010=>11100101
01010000=>00011000=>00011000=>00110000
01010001=>00110001=>10001100=>00011001
01010010=>10110000=>00001101=>00011010
01010011=>01100011=>11000110=>10001101
01010100=>01110000=>00001110=>00011100
01010101=>11100001=>10000111=>00001111
01010110=>11100010=>01000111=>10001110
01010111=>11000111=>11100011=>11000111
01011000=>00110010=>01001100=>10011000
01011001=>01100101=>10100110=>01001101
01011010=>11100100=>00100111=>01001110
01011011=>11001011=>11010011=>10100111
01011100=>01100110=>01100110=>11001100
01011101=>11001101=>10110011=>01100111
01011110=>11001110=>01110011=>11100110
01011111=>10011111=>11111001=>11110011
01100000=>00001010=>01010000=>10100000
01100001=>00010101=>10101000=>01010001
01100010=>10010100=>00101001=>01010010
01100011=>00101011=>11010100=>10101001
01100100=>01010100=>00101010=>01010100
01100101=>10101001=>10010101=>00101011
01100110=>10101010=>01010101=>10101010
01100111=>01010111=>11101010=>11010101
01101000=>00110100=>00101100=>01011000
01101001=>01101001=>10010110=>00101101
01101010=>11101000=>00010111=>00101110
01101011=>11010011=>11001011=>10010111
01101100=>01101010=>01010110=>10101100
01101101=>11010101=>10101011=>01010111
01101110=>11010110=>01101011=>11010110
01101111=>10101111=>11110101=>11101011
01110000=>00010110=>01101000=>11010000
01110001=>00101101=>10110100=>01101001
01110010=>10101100=>00110101=>01101010
01110011=>01011011=>11011010=>10110101
01110100=>01101100=>00110110=>01101100
01110101=>11011001=>10011011=>00110111
01110110=>11011010=>01011011=>10110110
01110111=>10110111=>11101101=>11011011
01111000=>00101110=>01110100=>11101000
01111001=>01011101=>10111010=>01110101
01111010=>11011100=>00111011=>01110110
01111011=>10111011=>11011101=>10111011
01111100=>01011110=>01111010=>11110100
01111101=>10111101=>10111101=>01111011
01111110=>10111110=>01111101=>11111010
01111111=>01111111=>11111110=>11111101
10000000=>00000010=>01000000=>10000000
10000001=>00000101=>10100000=>01000001
10000010=>10000100=>00100001=>01000010
10000011=>00001011=>11010000=>10100001
10000100=>01000100=>00100010=>01000100
10000101=>10001001=>10010001=>00100011
10000110=>10001010=>01010001=>10100010
10000111=>00010111=>11101000=>11010001
10001000=>00100100=>00100100=>01001000
10001001=>01001001=>10010010=>00100101
10001010=>11001000=>00010011=>00100110
10001011=>10010011=>11001001=>10010011
10001100=>01001010=>01010010=>10100100
10001101=>10010101=>10101001=>01010011
10001110=>10010110=>01101001=>11010010
10001111=>00101111=>11110100=>11101001
10010000=>00010100=>00101000=>01010000
10010001=>00101001=>10010100=>00101001
10010010=>10101000=>00010101=>00101010
10010011=>01010011=>11001010=>10010101
10010100=>01101000=>00010110=>00101100
10010101=>11010001=>10001011=>00010111
10010110=>11010010=>01001011=>10010110
10010111=>10100111=>11100101=>11001011
10011000=>00101010=>01010100=>10101000
10011001=>01010101=>10101010=>01010101
10011010=>11010100=>00101011=>01010110
10011011=>10101011=>11010101=>10101011
10011100=>01010110=>01101010=>11010100
10011101=>10101101=>10110101=>01101011
10011110=>10101110=>01110101=>11101010
10011111=>01011111=>11111010=>11110101
10100000=>00001100=>00110000=>01100000
10100001=>00011001=>10011000=>00110001
10100010=>10011000=>00011001=>00110010
10100011=>00110011=>11001100=>10011001
10100100=>01011000=>00011010=>00110100
10100101=>10110001=>10001101=>00011011
10100110=>10110010=>01001101=>10011010
10100111=>01100111=>11100110=>11001101
10101000=>00111000=>00011100=>00111000
10101001=>01110001=>10001110=>00011101
10101010=>11110000=>00001111=>00011110
10101011=>11100011=>11000111=>10001111
10101100=>01110010=>01001110=>10011100
10101101=>11100101=>10100111=>01001111
10101110=>11100110=>01100111=>11001110
10101111=>11001111=>11110011=>11100111
10110000=>00011010=>01011000=>10110000
10110001=>00110101=>10101100=>01011001
10110010=>10110100=>00101101=>01011010
10110011=>01101011=>11010110=>10101101
10110100=>01110100=>00101110=>01011100
10110101=>11101001=>10010111=>00101111
10110110=>11101010=>01010111=>10101110
10110111=>11010111=>11101011=>11010111
10111000=>00110110=>01101100=>11011000
10111001=>01101101=>10110110=>01101101
10111010=>11101100=>00110111=>01101110
10111011=>11011011=>11011011=>10110111
10111100=>01101110=>01110110=>11101100
10111101=>11011101=>10111011=>01110111
10111110=>11011110=>01111011=>11110110
10111111=>10111111=>11111101=>11111011
11000000=>00000110=>01100000=>11000000
11000001=>00001101=>10110000=>01100001
11000010=>10001100=>00110001=>01100010
11000011=>00011011=>11011000=>10110001
11000100=>01001100=>00110010=>01100100
11000101=>10011001=>10011001=>00110011
11000110=>10011010=>01011001=>10110010
11000111=>00110111=>11101100=>11011001
11001000=>00101100=>00110100=>01101000
11001001=>01011001=>10011010=>00110101
11001010=>11011000=>00011011=>00110110
11001011=>10110011=>11001101=>10011011
11001100=>01011010=>01011010=>10110100
11001101=>10110101=>10101101=>01011011
11001110=>10110110=>01101101=>11011010
11001111=>01101111=>11110110=>11101101
11010000=>00011100=>00111000=>01110000
11010001=>00111001=>10011100=>00111001
11010010=>10111000=>00011101=>00111010
11010011=>01110011=>11001110=>10011101
11010100=>01111000=>00011110=>00111100
11010101=>11110001=>10001111=>00011111
11010110=>11110010=>01001111=>10011110
11010111=>11100111=>11100111=>11001111
11011000=>00111010=>01011100=>10111000
11011001=>01110101=>10101110=>01011101
11011010=>11110100=>00101111=>01011110
11011011=>11101011=>11010111=>10101111
11011100=>01110110=>01101110=>11011100
11011101=>11101101=>10110111=>01101111
11011110=>11101110=>01110111=>11101110
11011111=>11011111=>11111011=>11110111
11100000=>00001110=>01110000=>11100000
11100001=>00011101=>10111000=>01110001
11100010=>10011100=>00111001=>01110010
11100011=>00111011=>11011100=>10111001
11100100=>01011100=>00111010=>01110100
11100101=>10111001=>10011101=>00111011
11100110=>10111010=>01011101=>10111010
11100111=>01110111=>11101110=>11011101
11101000=>00111100=>00111100=>01111000
11101001=>01111001=>10011110=>00111101
11101010=>11111000=>00011111=>00111110
11101011=>11110011=>11001111=>10011111
11101100=>01111010=>01011110=>10111100
11101101=>11110101=>10101111=>01011111
11101110=>11110110=>01101111=>11011110
11101111=>11101111=>11110111=>11101111
11110000=>00011110=>01111000=>11110000
11110001=>00111101=>10111100=>01111001
11110010=>10111100=>00111101=>01111010
11110011=>01111011=>11011110=>10111101
11110100=>01111100=>00111110=>01111100
11110101=>11111001=>10011111=>00111111
11110110=>11111010=>01011111=>10111110
11110111=>11110111=>11101111=>11011111
11111000=>00111110=>01111100=>11111000
11111001=>01111101=>10111110=>01111101
11111010=>11111100=>00111111=>01111110
11111011=>11111011=>11011111=>10111111
11111100=>01111110=>01111110=>11111100
11111101=>11111101=>10111111=>01111111
11111110=>11111110=>01111111=>11111110
11111111=>11111111=>11111111=>11111111
000000000=>000000000=>000000000=>000000000
000000001=>000000001=>100000000=>000000001
000000010=>100000000=>000000001=>000000010
000000011=>000000011=>110000000=>100000001
000000100=>010000000=>000000010=>000000100
000000101=>100000001=>100000001=>000000011
000000110=>100000010=>010000001=>100000010
000000111=>000000111=>111000000=>110000001
000001000=>001000000=>000000100=>000001000
000001001=>010000001=>100000010=>000000101
000001010=>110000000=>000000011=>000000110
000001011=>100000011=>110000001=>100000011
000001100=>010000010=>010000010=>100000100
000001101=>100000101=>101000001=>010000011
000001110=>100000110=>011000001=>110000010
000001111=>000001111=>111100000=>111000001
000010000=>000100000=>000001000=>000010000
000010001=>001000001=>100000100=>000001001
000010010=>101000000=>000000101=>000001010
000010011=>010000011=>110000010=>100000101
000010100=>011000000=>000000110=>000001100
000010101=>110000001=>100000011=>000000111
000010110=>110000010=>010000011=>100000110
000010111=>100000111=>111000001=>110000011
000011000=>001000010=>010000100=>100001000
000011001=>010000101=>101000010=>010000101
000011010=>110000100=>001000011=>010000110
000011011=>100001011=>110100001=>101000011
000011100=>010000110=>011000010=>110000100
000011101=>100001101=>101100001=>011000011
000011110=>100001110=>011100001=>111000010
000011111=>000011111=>111110000=>111100001
000100000=>000010000=>000010000=>000100000
000100001=>000100001=>100001000=>000010001
000100010=>100100000=>000001001=>000010010
000100011=>001000011=>110000100=>100001001
000100100=>010100000=>000001010=>000010100
000100101=>101000001=>100000101=>000001011
000100110=>101000010=>010000101=>100001010
000100111=>010000111=>111000010=>110000101
000101000=>001100000=>000001100=>000011000
000101001=>011000001=>100000110=>000001101
000101010=>111000000=>000000111=>000001110
000101011=>110000011=>110000011=>100000111
000101100=>011000010=>010000110=>100001100
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1011110000=>0001101110=>0111011000=>1110110000
1100101010=>1110110000=>0000110111=>0001101110
1100110010=>1010110100=>0010110101=>0101101010
1101001010=>1101110000=>0000111011=>0001110110
1101010010=>1011110000=>0000111101=>0001111010
1101010100=>0111110000=>0000111110=>0001111100
1110001010=>1100111000=>0001110011=>0011100110
1110010010=>1010111000=>0001110101=>0011101010
1110101000=>0011111000=>0001111100=>0011111000
1111000010=>1000111100=>0011110001=>0111100010
1111001000=>0010111100=>0011110100=>0111101000
1111010000=>0001111100=>0011111000=>0111110000
1111100000=>0000111110=>0111110000=>1111100000
101010101010=>111111000000=>000000111111=>000001111110
101010110010=>101111000100=>001000111101=>010001111010
101011001010=>110111001000=>000100111011=>001001110110
101011010010=>101111001000=>000100111101=>001001111010
101011110000=>000111001110=>011100111000=>111001110000
101100101010=>111011010000=>000010110111=>000101101110
101100110010=>101011010100=>001010110101=>010101101010
101101001010=>110111010000=>000010111011=>000101110110
101101010010=>101111010000=>000010111101=>000101111010
101110001010=>110011011000=>000110110011=>001101100110
101110010010=>101011011000=>000110110101=>001101101010
101111100000=>000011011110=>011110110000=>111101100000
110010101010=>111101100000=>000001101111=>000011011110
110010110010=>101101100100=>001001101101=>010011011010
110011001010=>110101101000=>000101101011=>001011010110
110011010010=>101101101000=>000101101101=>001011011010
110011011000=>001101101010=>010101101100=>101011011000
110011110000=>000101101110=>011101101000=>111011010000
110100101010=>111011100000=>000001110111=>000011101110
110100110010=>101011100100=>001001110101=>010011101010
110101001010=>110111100000=>000001111011=>000011110110
110101010010=>101111100000=>000001111101=>000011111010
110110001010=>110011101000=>000101110011=>001011100110
110110010010=>101011101000=>000101110101=>001011101010
110111100000=>000011101110=>011101110000=>111011100000
111000101010=>111001110000=>000011100111=>000111001110
111001001010=>110101110000=>000011101011=>000111010110
111001010010=>101101110000=>000011101101=>000111011010
111010001010=>110011110000=>000011110011=>000111100110
111010010010=>101011110000=>000011110101=>000111101010
111010101000=>001111110000=>000011111100=>000111111000
111101000010=>100011111000=>000111110001=>001111100010
111101001000=>001011111000=>000111110100=>001111101000
111101010000=>000111111000=>000111111000=>001111110000
111110000010=>100001111100=>001111100001=>011111000010
111110001000=>001001111100=>001111100100=>011111001000
111110010000=>000101111100=>001111101000=>011111010000
111110100000=>000011111100=>001111110000=>011111100000
111111000000=>000001111110=>011111100000=>111111000000
1111111111=>1111111111=>1111111111=>1111111111
1111111110=>1111111110=>0111111111=>1111111110
1111111001=>0111111101=>1011111110=>0111111101
1111101000=>0011111100=>0011111100=>0111111000
1111010100=>0111111000=>0001111110=>0011111100
1111000101=>1001111001=>1001111001=>0011110011
1110111110=>1111011110=>0111101111=>1111011110
1110101100=>0111110010=>0100111110=>1001111100
1110101010=>1111110000=>0000111111=>0001111110
1110101001=>0111110001=>1000111110=>0001111101
1110100101=>1011110001=>1000111101=>0001111011
1110000111=>0001110111=>1110111000=>1101110001
1101101001=>0111101001=>1001011110=>0010111101
1101011111=>1110011111=>1111100111=>1111001111
1101010101=>1111100001=>1000011111=>0000111111
1101010011=>0111100011=>1100011110=>1000111101
1101001101=>1011100101=>1010011101=>0100111011
1100101110=>1101100110=>0110011011=>1100110110
1100011110=>1001101110=>0111011001=>1110110010
1100011101=>1001101101=>1011011001=>0110110011
1100001111=>0001101111=>1111011000=>1110110001
1100001010=>1100011000=>0001100011=>0011000110
1100000110=>1000011010=>0101100001=>1011000010
1011111110=>1101111110=>0111111011=>1111110110
1011100101=>1011011001=>1001101101=>0011011011
1011100000=>0000110110=>0110110000=>1101100000
1011000111=>0011010111=>1110101100=>1101011001
1011000001=>0000110101=>1010110000=>0101100001
1010011101=>1011001101=>1011001101=>0110011011
1010010111=>1011000111=>1110001101=>1100011011
1010010010=>1010110000=>0000110101=>0001101010
1010010001=>0010110001=>1000110100=>0001101001
1010000101=>1000110001=>1000110001=>0001100011
1001111110=>1010111110=>0111110101=>1111101010
1001100111=>0101010111=>1110101010=>1101010101
1001100001=>0001010101=>1010101000=>0101010001
1001011000=>0011010010=>0100101100=>1001011000
1000111110=>1001011110=>0111101001=>1111010010
1000111000=>0010010110=>0110100100=>1101001000
1000110111=>1001010111=>1110101001=>1101010011
1000110001=>0010010101=>1010100100=>0101001001
1000101110=>1100100110=>0110010011=>1100100110
1000100101=>1010010001=>1000100101=>0001001011
1000011110=>1000101110=>0111010001=>1110100010
1000011001=>0100010101=>1010100010=>0101000101
1000010110=>1100010010=>0100100011=>1001000110
1000001110=>1000010110=>0110100001=>1101000010
1000000110=>1000001010=>0101000001=>1010000010
1000000010=>1000000100=>0010000001=>0100000010
10011111110=>10101111110=>01111110101=>11111101010
11111111110=>11111111110=>01111111111=>11111111110
0111111111=>0111111111=>1111111110=>1111111101
0111111101=>1011111101=>1011111101=>0111111011
0111100001=>0001011101=>1011101000=>0111010001
0111000001=>0000101101=>1011010000=>0110100001
0000000001=>0000000001=>1000000000=>0000000001
01111111111=>01111111111=>11111111110=>11111111101
0110100001=>0001101001=>1001011000=>0010110001
00000000001=>00000000001=>10000000000=>00000000001
0101000111=>0011000111=>1110001100=>1100011001
0100110011=>0101001011=>1101001010=>1010010101
0100100111=>0101000111=>1110001010=>1100010101
0100001111=>0001001111=>1111001000=>1110010001
0011000111=>0010010111=>1110100100=>1101001001
0010101011=>1110000011=>1100000111=>1000001111
0010001111=>0010001111=>1111000100=>1110001001
0001110011=>0100011011=>1101100010=>1011000101
0001100111=>0100010111=>1110100010=>1101000101
0001011011=>1100001011=>1101000011=>1010000111
0001010111=>1100000111=>1110000011=>1100000111
0001001111=>0100001111=>1111000010=>1110000101
0000111011=>1000011011=>1101100001=>1011000011
0000110111=>1000010111=>1110100001=>1101000011
0000101111=>1000001111=>1111000001=>1110000011
0000011111=>0000011111=>1111100000=>1111000001
010101010101=>111110000001=>100000011111=>000000111111
010101001101=>101110000101=>101000011101=>010000111011
010101000111=>001110000111=>111000011100=>110000111001
010100110101=>110110001001=>100100011011=>001000110111
010100101101=>110110000101=>101000011011=>010000110111
010100011101=>100110001101=>101100011001=>011000110011
010100010111=>100110000111=>111000011001=>110000110011
010100001111=>000110001111=>111100011000=>111000110001
010011010101=>111010010001=>100010010111=>000100101111
010011001101=>101010010101=>101010010101=>010100101011
010011000111=>001010010111=>111010010100=>110100101001
010010110101=>111010001001=>100100010111=>001000101111
010010101101=>111010000101=>101000010111=>010000101111
010010001111=>001010001111=>111100010100=>111000101001
010001110101=>110010011001=>100110010011=>001100100111
010001110011=>010010011011=>110110010010=>101100100101
010001100111=>010010010111=>111010010010=>110100100101
010001011101=>110010001101=>101100010011=>011000100111
010001001111=>010010001111=>111100010010=>111000100101
010000111101=>100010011101=>101110010001=>011100100011
010000111011=>100010011011=>110110010001=>101100100011
010000110111=>100010010111=>111010010001=>110100100011
010000101111=>100010001111=>111100010001=>111000100011
010000011111=>000010011111=>111110010000=>111100100001
001101001101=>101100100101=>101001001101=>010010011011
001101000111=>001100100111=>111001001100=>110010011001
001100110011=>010100101011=>110101001010=>101010010101
001100100111=>010100100111=>111001001010=>110010010101
001100001111=>000100101111=>111101001000=>111010010001
001011000111=>001100010111=>111010001100=>110100011001
001010101011=>111100000011=>110000001111=>100000011111
001010011101=>101100001101=>101100001101=>011000011011
001010010111=>101100000111=>111000001101=>110000011011
001010001111=>001100001111=>111100001100=>111000011001
001001110011=>010100011011=>110110001010=>101100010101
001001100111=>010100010111=>111010001010=>110100010101
001001001111=>010100001111=>111100001010=>111000010101
001000011111=>000100011111=>111110001000=>111100010001
000111010101=>111000110001=>100011000111=>000110001111
000111001101=>101000110101=>101011000101=>010110001011
000111000111=>001000110111=>111011000100=>110110001001
000110110101=>111000101001=>100101000111=>001010001111
000110101101=>111000100101=>101001000111=>010010001111
000110001111=>001000101111=>111101000100=>111010001001
000101110101=>111000011001=>100110000111=>001100001111
000101101101=>111000010101=>101010000111=>010100001111
000101011101=>111000001101=>101100000111=>011000001111
000101011011=>111000001011=>110100000111=>101000001111
000101010111=>111000000111=>111000000111=>110000001111
000100111101=>101000011101=>101110000101=>011100001011
000100110111=>101000010111=>111010000101=>110100001011
000100011111=>001000011111=>111110000100=>111100001001
000011110011=>010000111011=>110111000010=>101110000101
000011101101=>110000110101=>101011000011=>010110000111
000011101011=>110000110011=>110011000011=>100110000111
000011100111=>010000110111=>111011000010=>110110000101
000011011101=>110000101101=>101101000011=>011010000111
000011011011=>110000101011=>110101000011=>101010000111
000011010111=>110000100111=>111001000011=>110010000111
000011001111=>010000101111=>111101000010=>111010000101
000010111011=>110000011011=>110110000011=>101100000111
000010110111=>110000010111=>111010000011=>110100000111
000010101111=>110000001111=>111100000011=>111000000111
000010011111=>010000011111=>111110000010=>111100000101
000001111101=>100000111101=>101111000001=>011110000011
000001111011=>100000111011=>110111000001=>101110000011
000001110111=>100000110111=>111011000001=>110110000011
000001101111=>100000101111=>111101000001=>111010000011
000001011111=>100000011111=>111110000001=>111100000011
000000111111=>000000111111=>111111000000=>111110000001
111111111111=>111111111111=>111111111111=>111111111111
111110100101=>101111110001=>100011111101=>000111111011
111001100001=>000101110101=>101011101000=>010111010001
111000000111=>000001110111=>111011100000=>110111000001
111000110001=>001001110101=>101011100100=>010111001001
111000100101=>101001110001=>100011100101=>000111001011
111011100101=>101111011001=>100110111101=>001101111011
111010010111=>101111000111=>111000111101=>110001111011
111010011101=>101111001101=>101100111101=>011001111011
111010000101=>100011110001=>100011110001=>000111100011
100111100001=>000101011101=>101110101000=>011101010001
100110011001=>010101010101=>101010101010=>010101010101
100110000111=>000101010111=>111010101000=>110101010001
100001111001=>010001011101=>101110100010=>011101000101
100001100111=>010001010111=>111010100010=>110101000101
100000011111=>000001011111=>111110100000=>111101000001
100000110111=>100001010111=>111010100001=>110101000011
100000111101=>100001011101=>101110100001=>011101000011
100000100101=>101000010001=>100010000101=>000100001011
100011000111=>001001010111=>111010100100=>110101001001
100011110001=>001001011101=>101110100100=>011101001001
100011100101=>101001011001=>100110100101=>001101001011
100010010111=>101001000111=>111000100101=>110001001011
100010011101=>101001001101=>101100100101=>011001001011
100010000101=>100010010001=>100010010001=>000100100011
101100011001=>010011010101=>101010110010=>010101100101
101100110001=>001011010101=>101010110100=>010101101001
101100100101=>101011010001=>100010110101=>000101101011
101111100101=>101101111001=>100111101101=>001111011011
101110010111=>101101100111=>111001101101=>110011011011
101110011101=>101101101101=>101101101101=>011011011011
101110000101=>100011011001=>100110110001=>001101100011
101001011111=>101100011111=>111110001101=>111100011011
101001001101=>101011000101=>101000110101=>010001101011
101001110111=>101100110111=>111011001101=>110110011011
101001110001=>001011001101=>101100110100=>011001101001
101001111101=>101100111101=>101111001101=>011110011011
101000010111=>100011000111=>111000110001=>110001100011
101000011101=>100011001101=>101100110001=>011001100011
101000000101=>100000110001=>100011000001=>000110000011
0000000000=>0000000000=>0000000000=>0000000000
0000011110=>1000001110=>0111000001=>1110000010
0001111110=>1000111110=>0111110001=>1111100010
0111111110=>1011111110=>0111111101=>1111111010
0100111110=>1010011110=>0111100101=>1111001010
000000000000=>000000000000=>000000000000=>000000000000
0101010100=>0111100000=>0000011110=>0000111100
0000000010=>1000000000=>0000000001=>0000000010
0000001110=>1000000110=>0110000001=>1100000010
0000111110=>1000011110=>0111100001=>1111000010
0011111110=>1001111110=>0111111001=>1111110010
00000000010=>10000000000=>00000000001=>00000000010
0000000100=>0100000000=>0000000010=>0000000100
00000001110=>10000000110=>01100000001=>11000000010
00000111110=>10000011110=>01111000001=>11110000010
0001011110=>1100001110=>0111000011=>1110000110
0010111110=>1100011110=>0111100011=>1111000110
00011111110=>10001111110=>01111110001=>11111100010
01111111110=>10111111110=>01111111101=>11111111010
001100111000=>001010010110=>011010010100=>110100101000
001111000100=>010010011100=>001110010010=>011100100100
001111001000=>001010011100=>001110010100=>011100101000
010011001100=>010101001010=>010100101010=>101001010100
010011011000=>001101001010=>010100101100=>101001011000
010011100100=>010101001100=>001100101010=>011001010100
010011101000=>001101001100=>001100101100=>011001011000
010100111000=>001011000110=>011000110100=>110001101000
010110001100=>010011001010=>010100110010=>101001100100
010110011000=>001011001010=>010100110100=>101001101000
010111000100=>010011001100=>001100110010=>011001100100
010111001000=>001011001100=>001100110100=>011001101000
011001001100=>010101010010=>010010101010=>100101010100
011001011000=>001101010010=>010010101100=>100101011000
011001100100=>010101010100=>001010101010=>010101010100
011001101000=>001101010100=>001010101100=>010101011000
011010001100=>010011010010=>010010110010=>100101100100
011010011000=>001011010010=>010010110100=>100101101000
011011000100=>010011010100=>001010110010=>010101100100
011011001000=>001011010100=>001010110100=>010101101000
011100011000=>001001011010=>010110100100=>101101001000
011110000100=>010001011100=>001110100010=>011101000100
011110001000=>001001011100=>001110100100=>011101001000
011110010000=>000101011100=>001110101000=>011101010000
0100101111=>1010001111=>1111000101=>1110001011
0110011001=>0101010101=>1010101010=>0101010101
0110110001=>0011010101=>1010101100=>0101011001
011100011001=>010010110101=>101011010010=>010110100101
011101100001=>000110110101=>101011011000=>010110110001
0000000101=>1000000001=>1000000001=>0000000011
0001111101=>1000111101=>1011110001=>0111100011
0000010001=>0010000001=>1000000100=>0000001001
11111111111=>11111111111=>11111111111=>11111111111
101000111001=>010011001101=>101100110010=>011001100101
100100111001=>010101001101=>101100101010=>011001010101
101001100011=>001011001011=>110100110100=>101001101001
101000110011=>010011001011=>110100110010=>101001100101
100100110011=>010101001011=>110100101010=>101001010101
101010000111=>000111000111=>111000111000=>110001110001
101000100111=>010011000111=>111000110010=>110001100101
110111000101=>100111011001=>100110111001=>001101110011
0110010011=>0101010011=>1100101010=>1001010101
101100010011=>010011010011=>110010110010=>100101100101
011100000111=>000010110111=>111011010000=>110110100001
110100110101=>110111001001=>100100111011=>001001110111
110001110101=>110011011001=>100110110011=>001101100111
110100011101=>100111001101=>101100111001=>011001110011
110000111101=>100011011101=>101110110001=>011101100011
101100011011=>100110101011=>110101011001=>101010110011
100110011011=>101010101011=>110101010101=>101010101011
101000111011=>100110011011=>110110011001=>101100110011
100100111011=>101010011011=>110110010101=>101100101011
101100010111=>100110100111=>111001011001=>110010110011
100110010111=>101010100111=>111001010101=>110010101011
101000110111=>100110010111=>111010011001=>110100110011
100100110111=>101010010111=>111010010101=>110100101011
101000101111=>100110001111=>111100011001=>111000110011
100100101111=>101010001111=>111100010101=>111000101011
0000000011=>0000000011=>1100000000=>1000000001
0000111111=>0000111111=>1111110000=>1111100001
00000000011=>00000000011=>11000000000=>10000000001
0001101111=>1000101111=>1111010001=>1110100011
0100101001=>0110100001=>1000010110=>0000101101
0100111011=>1010011011=>1101100101=>1011001011
011010110111=>111010010111=>111010010111=>110100101111
101101000011=>000111010011=>110010111000=>100101110001
0001010101=>1110000001=>1000000111=>0000001111
0011010111=>1100100111=>1110010011=>1100100111
0111010101=>1110110001=>1000110111=>0001101111
0001110111=>1000110111=>1110110001=>1101100011
000000000101=>100000000001=>100000000001=>000000000011
010101110111=>111000110111=>111011000111=>110110001111
000001010101=>111000000001=>100000000111=>000000001111
011101010111=>111011000111=>111000110111=>110001101111
011101110101=>111011011001=>100110110111=>001101101111
011111011111=>101111011111=>111110111101=>111101111011
0110011011=>1010101011=>1101010101=>1010101011
111000110101=>110011101001=>100101110011=>001011100111
111100001101=>100011110101=>101011110001=>010111100011
0100111001=>0101001101=>1011001010=>0110010101
0101100001=>0001100101=>1010011000=>0100110001
0100110001=>0010100101=>1010010100=>0100101001
0110100011=>0011010011=>1100101100=>1001011001
0110010111=>1010100111=>1110010101=>1100101011
0100110111=>1010010111=>1110100101=>1101001011
0001010000=>0001100000=>0000011000=>0000110000
0101000101=>1001100001=>1000011001=>0000110011
0110001001=>0100101001=>1001010010=>0010100101
010100000101=>100001100001=>100001100001=>000011000011
000101000101=>100110000001=>100000011001=>000000110011
0011011110=>1100101110=>0111010011=>1110100110
0011101110=>1100110110=>0110110011=>1101100110
0011110110=>1100111010=>0101110011=>1011100110
0111001101=>1010110101=>1010110101=>0101101011
111000011101=>100011101101=>101101110001=>011011100011
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
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.
This is the word obtained by moving the first letter to the end.
searching the database
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