Identifier
Mp00096:
Binary words
—Foata bijection⟶
Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Images
=>
0=>0=>1=>1
1=>1=>0=>0
00=>00=>11=>11
01=>01=>10=>01
10=>10=>01=>10
11=>11=>00=>00
000=>000=>111=>111
001=>001=>110=>011
010=>100=>011=>101
011=>011=>100=>010
100=>010=>101=>110
101=>101=>010=>001
110=>110=>001=>100
111=>111=>000=>000
0000=>0000=>1111=>1111
0001=>0001=>1110=>0111
0010=>1000=>0111=>1011
0011=>0011=>1100=>0110
0100=>0100=>1011=>1101
0101=>1001=>0110=>0011
0110=>1010=>0101=>1010
0111=>0111=>1000=>0100
1000=>0010=>1101=>1110
1001=>0101=>1010=>0101
1010=>1100=>0011=>1001
1011=>1011=>0100=>0010
1100=>0110=>1001=>1100
1101=>1101=>0010=>0001
1110=>1110=>0001=>1000
1111=>1111=>0000=>0000
00000=>00000=>11111=>11111
00001=>00001=>11110=>01111
00010=>10000=>01111=>10111
00011=>00011=>11100=>01110
00100=>01000=>10111=>11011
00101=>10001=>01110=>00111
00110=>10010=>01101=>10110
00111=>00111=>11000=>01100
01000=>00100=>11011=>11101
01001=>01001=>10110=>01011
01010=>11000=>00111=>10011
01011=>10011=>01100=>00110
01100=>01010=>10101=>11010
01101=>10101=>01010=>00101
01110=>10110=>01001=>10100
01111=>01111=>10000=>01000
10000=>00010=>11101=>11110
10001=>00101=>11010=>01101
10010=>10100=>01011=>10101
10011=>01011=>10100=>01010
10100=>01100=>10011=>11001
10101=>11001=>00110=>00011
10110=>11010=>00101=>10010
10111=>10111=>01000=>00100
11000=>00110=>11001=>11100
11001=>01101=>10010=>01001
11010=>11100=>00011=>10001
11011=>11011=>00100=>00010
11100=>01110=>10001=>11000
11101=>11101=>00010=>00001
11110=>11110=>00001=>10000
11111=>11111=>00000=>00000
000000=>000000=>111111=>111111
000001=>000001=>111110=>011111
000010=>100000=>011111=>101111
000011=>000011=>111100=>011110
000100=>010000=>101111=>110111
000101=>100001=>011110=>001111
000110=>100010=>011101=>101110
000111=>000111=>111000=>011100
001000=>001000=>110111=>111011
001001=>010001=>101110=>010111
001010=>110000=>001111=>100111
001011=>100011=>011100=>001110
001100=>010010=>101101=>110110
001101=>100101=>011010=>001101
001110=>100110=>011001=>101100
001111=>001111=>110000=>011000
010000=>000100=>111011=>111101
010001=>001001=>110110=>011011
010010=>101000=>010111=>101011
010011=>010011=>101100=>010110
010100=>011000=>100111=>110011
010101=>110001=>001110=>000111
010110=>110010=>001101=>100110
010111=>100111=>011000=>001100
011000=>001010=>110101=>111010
011001=>010101=>101010=>010101
011010=>110100=>001011=>100101
011011=>101011=>010100=>001010
011100=>010110=>101001=>110100
011101=>101101=>010010=>001001
011110=>101110=>010001=>101000
011111=>011111=>100000=>010000
100000=>000010=>111101=>111110
100001=>000101=>111010=>011101
100010=>100100=>011011=>101101
100011=>001011=>110100=>011010
100100=>010100=>101011=>110101
100101=>101001=>010110=>001011
100110=>101010=>010101=>101010
100111=>010111=>101000=>010100
101000=>001100=>110011=>111001
101001=>011001=>100110=>010011
101010=>111000=>000111=>100011
101011=>110011=>001100=>000110
101100=>011010=>100101=>110010
101101=>110101=>001010=>000101
101110=>110110=>001001=>100100
101111=>101111=>010000=>001000
110000=>000110=>111001=>111100
110001=>001101=>110010=>011001
110010=>101100=>010011=>101001
110011=>011011=>100100=>010010
110100=>011100=>100011=>110001
110101=>111001=>000110=>000011
110110=>111010=>000101=>100010
110111=>110111=>001000=>000100
111000=>001110=>110001=>111000
111001=>011101=>100010=>010001
111010=>111100=>000011=>100001
111011=>111011=>000100=>000010
111100=>011110=>100001=>110000
111101=>111101=>000010=>000001
111110=>111110=>000001=>100000
111111=>111111=>000000=>000000
0000000=>0000000=>1111111=>1111111
0000001=>0000001=>1111110=>0111111
0000010=>1000000=>0111111=>1011111
0000011=>0000011=>1111100=>0111110
0000100=>0100000=>1011111=>1101111
0000101=>1000001=>0111110=>0011111
0000110=>1000010=>0111101=>1011110
0000111=>0000111=>1111000=>0111100
0001000=>0010000=>1101111=>1110111
0001001=>0100001=>1011110=>0101111
0001010=>1100000=>0011111=>1001111
0001011=>1000011=>0111100=>0011110
0001100=>0100010=>1011101=>1101110
0001101=>1000101=>0111010=>0011101
0001110=>1000110=>0111001=>1011100
0001111=>0001111=>1110000=>0111000
0010000=>0001000=>1110111=>1111011
0010001=>0010001=>1101110=>0110111
0010010=>1010000=>0101111=>1010111
0010011=>0100011=>1011100=>0101110
0010100=>0110000=>1001111=>1100111
0010101=>1100001=>0011110=>0001111
0010110=>1100010=>0011101=>1001110
0010111=>1000111=>0111000=>0011100
0011000=>0010010=>1101101=>1110110
0011001=>0100101=>1011010=>0101101
0011010=>1100100=>0011011=>1001101
0011011=>1001011=>0110100=>0011010
0011100=>0100110=>1011001=>1101100
0011101=>1001101=>0110010=>0011001
0011110=>1001110=>0110001=>1011000
0011111=>0011111=>1100000=>0110000
0100000=>0000100=>1111011=>1111101
0100001=>0001001=>1110110=>0111011
0100010=>1001000=>0110111=>1011011
0100011=>0010011=>1101100=>0110110
0100100=>0101000=>1010111=>1101011
0100101=>1010001=>0101110=>0010111
0100110=>1010010=>0101101=>1010110
0100111=>0100111=>1011000=>0101100
0101000=>0011000=>1100111=>1110011
0101001=>0110001=>1001110=>0100111
0101010=>1110000=>0001111=>1000111
0101011=>1100011=>0011100=>0001110
0101100=>0110010=>1001101=>1100110
0101101=>1100101=>0011010=>0001101
0101110=>1100110=>0011001=>1001100
0101111=>1001111=>0110000=>0011000
0110000=>0001010=>1110101=>1111010
0110001=>0010101=>1101010=>0110101
0110010=>1010100=>0101011=>1010101
0110011=>0101011=>1010100=>0101010
0110100=>0110100=>1001011=>1100101
0110101=>1101001=>0010110=>0001011
0110110=>1101010=>0010101=>1001010
0110111=>1010111=>0101000=>0010100
0111000=>0010110=>1101001=>1110100
0111001=>0101101=>1010010=>0101001
0111010=>1101100=>0010011=>1001001
0111011=>1011011=>0100100=>0010010
0111100=>0101110=>1010001=>1101000
0111101=>1011101=>0100010=>0010001
0111110=>1011110=>0100001=>1010000
0111111=>0111111=>1000000=>0100000
1000000=>0000010=>1111101=>1111110
1000001=>0000101=>1111010=>0111101
1000010=>1000100=>0111011=>1011101
1000011=>0001011=>1110100=>0111010
1000100=>0100100=>1011011=>1101101
1000101=>1001001=>0110110=>0011011
1000110=>1001010=>0110101=>1011010
1000111=>0010111=>1101000=>0110100
1001000=>0010100=>1101011=>1110101
1001001=>0101001=>1010110=>0101011
1001010=>1101000=>0010111=>1001011
1001011=>1010011=>0101100=>0010110
1001100=>0101010=>1010101=>1101010
1001101=>1010101=>0101010=>0010101
1001110=>1010110=>0101001=>1010100
1001111=>0101111=>1010000=>0101000
1010000=>0001100=>1110011=>1111001
1010001=>0011001=>1100110=>0110011
1010010=>1011000=>0100111=>1010011
1010011=>0110011=>1001100=>0100110
1010100=>0111000=>1000111=>1100011
1010101=>1110001=>0001110=>0000111
1010110=>1110010=>0001101=>1000110
1010111=>1100111=>0011000=>0001100
1011000=>0011010=>1100101=>1110010
1011001=>0110101=>1001010=>0100101
1011010=>1110100=>0001011=>1000101
1011011=>1101011=>0010100=>0001010
1011100=>0110110=>1001001=>1100100
1011101=>1101101=>0010010=>0001001
1011110=>1101110=>0010001=>1001000
1011111=>1011111=>0100000=>0010000
1100000=>0000110=>1111001=>1111100
1100001=>0001101=>1110010=>0111001
1100010=>1001100=>0110011=>1011001
1100011=>0011011=>1100100=>0110010
1100100=>0101100=>1010011=>1101001
1100101=>1011001=>0100110=>0010011
1100110=>1011010=>0100101=>1010010
1100111=>0110111=>1001000=>0100100
1101000=>0011100=>1100011=>1110001
1101001=>0111001=>1000110=>0100011
1101010=>1111000=>0000111=>1000011
1101011=>1110011=>0001100=>0000110
1101100=>0111010=>1000101=>1100010
1101101=>1110101=>0001010=>0000101
1101110=>1110110=>0001001=>1000100
1101111=>1101111=>0010000=>0001000
1110000=>0001110=>1110001=>1111000
1110001=>0011101=>1100010=>0110001
1110010=>1011100=>0100011=>1010001
1110011=>0111011=>1000100=>0100010
1110100=>0111100=>1000011=>1100001
1110101=>1111001=>0000110=>0000011
1110110=>1111010=>0000101=>1000010
1110111=>1110111=>0001000=>0000100
1111000=>0011110=>1100001=>1110000
1111001=>0111101=>1000010=>0100001
1111010=>1111100=>0000011=>1000001
1111011=>1111011=>0000100=>0000010
1111100=>0111110=>1000001=>1100000
1111101=>1111101=>0000010=>0000001
1111110=>1111110=>0000001=>1000000
1111111=>1111111=>0000000=>0000000
00000000=>00000000=>11111111=>11111111
00000001=>00000001=>11111110=>01111111
00000010=>10000000=>01111111=>10111111
00000011=>00000011=>11111100=>01111110
00000100=>01000000=>10111111=>11011111
00000101=>10000001=>01111110=>00111111
00000110=>10000010=>01111101=>10111110
00000111=>00000111=>11111000=>01111100
00001000=>00100000=>11011111=>11101111
00001001=>01000001=>10111110=>01011111
00001010=>11000000=>00111111=>10011111
00001011=>10000011=>01111100=>00111110
00001100=>01000010=>10111101=>11011110
00001101=>10000101=>01111010=>00111101
00001110=>10000110=>01111001=>10111100
00001111=>00001111=>11110000=>01111000
00010000=>00010000=>11101111=>11110111
00010001=>00100001=>11011110=>01101111
00010010=>10100000=>01011111=>10101111
00010011=>01000011=>10111100=>01011110
00010100=>01100000=>10011111=>11001111
00010101=>11000001=>00111110=>00011111
00010110=>11000010=>00111101=>10011110
00010111=>10000111=>01111000=>00111100
00011000=>00100010=>11011101=>11101110
00011001=>01000101=>10111010=>01011101
00011010=>11000100=>00111011=>10011101
00011011=>10001011=>01110100=>00111010
00011100=>01000110=>10111001=>11011100
00011101=>10001101=>01110010=>00111001
00011110=>10001110=>01110001=>10111000
00011111=>00011111=>11100000=>01110000
00100000=>00001000=>11110111=>11111011
00100001=>00010001=>11101110=>01110111
00100010=>10010000=>01101111=>10110111
00100011=>00100011=>11011100=>01101110
00100100=>01010000=>10101111=>11010111
00100101=>10100001=>01011110=>00101111
00100110=>10100010=>01011101=>10101110
00100111=>01000111=>10111000=>01011100
00101000=>00110000=>11001111=>11100111
00101001=>01100001=>10011110=>01001111
00101010=>11100000=>00011111=>10001111
00101011=>11000011=>00111100=>00011110
00101100=>01100010=>10011101=>11001110
00101101=>11000101=>00111010=>00011101
00101110=>11000110=>00111001=>10011100
00101111=>10001111=>01110000=>00111000
00110000=>00010010=>11101101=>11110110
00110001=>00100101=>11011010=>01101101
00110010=>10100100=>01011011=>10101101
00110011=>01001011=>10110100=>01011010
00110100=>01100100=>10011011=>11001101
00110101=>11001001=>00110110=>00011011
00110110=>11001010=>00110101=>10011010
00110111=>10010111=>01101000=>00110100
00111000=>00100110=>11011001=>11101100
00111001=>01001101=>10110010=>01011001
00111010=>11001100=>00110011=>10011001
00111011=>10011011=>01100100=>00110010
00111100=>01001110=>10110001=>11011000
00111101=>10011101=>01100010=>00110001
00111110=>10011110=>01100001=>10110000
00111111=>00111111=>11000000=>01100000
01000000=>00000100=>11111011=>11111101
01000001=>00001001=>11110110=>01111011
01000010=>10001000=>01110111=>10111011
01000011=>00010011=>11101100=>01110110
01000100=>01001000=>10110111=>11011011
01000101=>10010001=>01101110=>00110111
01000110=>10010010=>01101101=>10110110
01000111=>00100111=>11011000=>01101100
01001000=>00101000=>11010111=>11101011
01001001=>01010001=>10101110=>01010111
01001010=>11010000=>00101111=>10010111
01001011=>10100011=>01011100=>00101110
01001100=>01010010=>10101101=>11010110
01001101=>10100101=>01011010=>00101101
01001110=>10100110=>01011001=>10101100
01001111=>01001111=>10110000=>01011000
01010000=>00011000=>11100111=>11110011
01010001=>00110001=>11001110=>01100111
01010010=>10110000=>01001111=>10100111
01010011=>01100011=>10011100=>01001110
01010100=>01110000=>10001111=>11000111
01010101=>11100001=>00011110=>00001111
01010110=>11100010=>00011101=>10001110
01010111=>11000111=>00111000=>00011100
01011000=>00110010=>11001101=>11100110
01011001=>01100101=>10011010=>01001101
01011010=>11100100=>00011011=>10001101
01011011=>11001011=>00110100=>00011010
01011100=>01100110=>10011001=>11001100
01011101=>11001101=>00110010=>00011001
01011110=>11001110=>00110001=>10011000
01011111=>10011111=>01100000=>00110000
01100000=>00001010=>11110101=>11111010
01100001=>00010101=>11101010=>01110101
01100010=>10010100=>01101011=>10110101
01100011=>00101011=>11010100=>01101010
01100100=>01010100=>10101011=>11010101
01100101=>10101001=>01010110=>00101011
01100110=>10101010=>01010101=>10101010
01100111=>01010111=>10101000=>01010100
01101000=>00110100=>11001011=>11100101
01101001=>01101001=>10010110=>01001011
01101010=>11101000=>00010111=>10001011
01101011=>11010011=>00101100=>00010110
01101100=>01101010=>10010101=>11001010
01101101=>11010101=>00101010=>00010101
01101110=>11010110=>00101001=>10010100
01101111=>10101111=>01010000=>00101000
01110000=>00010110=>11101001=>11110100
01110001=>00101101=>11010010=>01101001
01110010=>10101100=>01010011=>10101001
01110011=>01011011=>10100100=>01010010
01110100=>01101100=>10010011=>11001001
01110101=>11011001=>00100110=>00010011
01110110=>11011010=>00100101=>10010010
01110111=>10110111=>01001000=>00100100
01111000=>00101110=>11010001=>11101000
01111001=>01011101=>10100010=>01010001
01111010=>11011100=>00100011=>10010001
01111011=>10111011=>01000100=>00100010
01111100=>01011110=>10100001=>11010000
01111101=>10111101=>01000010=>00100001
01111110=>10111110=>01000001=>10100000
01111111=>01111111=>10000000=>01000000
10000000=>00000010=>11111101=>11111110
10000001=>00000101=>11111010=>01111101
10000010=>10000100=>01111011=>10111101
10000011=>00001011=>11110100=>01111010
10000100=>01000100=>10111011=>11011101
10000101=>10001001=>01110110=>00111011
10000110=>10001010=>01110101=>10111010
10000111=>00010111=>11101000=>01110100
10001000=>00100100=>11011011=>11101101
10001001=>01001001=>10110110=>01011011
10001010=>11001000=>00110111=>10011011
10001011=>10010011=>01101100=>00110110
10001100=>01001010=>10110101=>11011010
10001101=>10010101=>01101010=>00110101
10001110=>10010110=>01101001=>10110100
10001111=>00101111=>11010000=>01101000
10010000=>00010100=>11101011=>11110101
10010001=>00101001=>11010110=>01101011
10010010=>10101000=>01010111=>10101011
10010011=>01010011=>10101100=>01010110
10010100=>01101000=>10010111=>11001011
10010101=>11010001=>00101110=>00010111
10010110=>11010010=>00101101=>10010110
10010111=>10100111=>01011000=>00101100
10011000=>00101010=>11010101=>11101010
10011001=>01010101=>10101010=>01010101
10011010=>11010100=>00101011=>10010101
10011011=>10101011=>01010100=>00101010
10011100=>01010110=>10101001=>11010100
10011101=>10101101=>01010010=>00101001
10011110=>10101110=>01010001=>10101000
10011111=>01011111=>10100000=>01010000
10100000=>00001100=>11110011=>11111001
10100001=>00011001=>11100110=>01110011
10100010=>10011000=>01100111=>10110011
10100011=>00110011=>11001100=>01100110
10100100=>01011000=>10100111=>11010011
10100101=>10110001=>01001110=>00100111
10100110=>10110010=>01001101=>10100110
10100111=>01100111=>10011000=>01001100
10101000=>00111000=>11000111=>11100011
10101001=>01110001=>10001110=>01000111
10101010=>11110000=>00001111=>10000111
10101011=>11100011=>00011100=>00001110
10101100=>01110010=>10001101=>11000110
10101101=>11100101=>00011010=>00001101
10101110=>11100110=>00011001=>10001100
10101111=>11001111=>00110000=>00011000
10110000=>00011010=>11100101=>11110010
10110001=>00110101=>11001010=>01100101
10110010=>10110100=>01001011=>10100101
10110011=>01101011=>10010100=>01001010
10110100=>01110100=>10001011=>11000101
10110101=>11101001=>00010110=>00001011
10110110=>11101010=>00010101=>10001010
10110111=>11010111=>00101000=>00010100
10111000=>00110110=>11001001=>11100100
10111001=>01101101=>10010010=>01001001
10111010=>11101100=>00010011=>10001001
10111011=>11011011=>00100100=>00010010
10111100=>01101110=>10010001=>11001000
10111101=>11011101=>00100010=>00010001
10111110=>11011110=>00100001=>10010000
10111111=>10111111=>01000000=>00100000
11000000=>00000110=>11111001=>11111100
11000001=>00001101=>11110010=>01111001
11000010=>10001100=>01110011=>10111001
11000011=>00011011=>11100100=>01110010
11000100=>01001100=>10110011=>11011001
11000101=>10011001=>01100110=>00110011
11000110=>10011010=>01100101=>10110010
11000111=>00110111=>11001000=>01100100
11001000=>00101100=>11010011=>11101001
11001001=>01011001=>10100110=>01010011
11001010=>11011000=>00100111=>10010011
11001011=>10110011=>01001100=>00100110
11001100=>01011010=>10100101=>11010010
11001101=>10110101=>01001010=>00100101
11001110=>10110110=>01001001=>10100100
11001111=>01101111=>10010000=>01001000
11010000=>00011100=>11100011=>11110001
11010001=>00111001=>11000110=>01100011
11010010=>10111000=>01000111=>10100011
11010011=>01110011=>10001100=>01000110
11010100=>01111000=>10000111=>11000011
11010101=>11110001=>00001110=>00000111
11010110=>11110010=>00001101=>10000110
11010111=>11100111=>00011000=>00001100
11011000=>00111010=>11000101=>11100010
11011001=>01110101=>10001010=>01000101
11011010=>11110100=>00001011=>10000101
11011011=>11101011=>00010100=>00001010
11011100=>01110110=>10001001=>11000100
11011101=>11101101=>00010010=>00001001
11011110=>11101110=>00010001=>10001000
11011111=>11011111=>00100000=>00010000
11100000=>00001110=>11110001=>11111000
11100001=>00011101=>11100010=>01110001
11100010=>10011100=>01100011=>10110001
11100011=>00111011=>11000100=>01100010
11100100=>01011100=>10100011=>11010001
11100101=>10111001=>01000110=>00100011
11100110=>10111010=>01000101=>10100010
11100111=>01110111=>10001000=>01000100
11101000=>00111100=>11000011=>11100001
11101001=>01111001=>10000110=>01000011
11101010=>11111000=>00000111=>10000011
11101011=>11110011=>00001100=>00000110
11101100=>01111010=>10000101=>11000010
11101101=>11110101=>00001010=>00000101
11101110=>11110110=>00001001=>10000100
11101111=>11101111=>00010000=>00001000
11110000=>00011110=>11100001=>11110000
11110001=>00111101=>11000010=>01100001
11110010=>10111100=>01000011=>10100001
11110011=>01111011=>10000100=>01000010
11110100=>01111100=>10000011=>11000001
11110101=>11111001=>00000110=>00000011
11110110=>11111010=>00000101=>10000010
11110111=>11110111=>00001000=>00000100
11111000=>00111110=>11000001=>11100000
11111001=>01111101=>10000010=>01000001
11111010=>11111100=>00000011=>10000001
11111011=>11111011=>00000100=>00000010
11111100=>01111110=>10000001=>11000000
11111101=>11111101=>00000010=>00000001
11111110=>11111110=>00000001=>10000000
11111111=>11111111=>00000000=>00000000
000000000=>000000000=>111111111=>111111111
000000001=>000000001=>111111110=>011111111
000000010=>100000000=>011111111=>101111111
000000011=>000000011=>111111100=>011111110
000000100=>010000000=>101111111=>110111111
000000101=>100000001=>011111110=>001111111
000000110=>100000010=>011111101=>101111110
000000111=>000000111=>111111000=>011111100
000001000=>001000000=>110111111=>111011111
000001001=>010000001=>101111110=>010111111
000001010=>110000000=>001111111=>100111111
000001011=>100000011=>011111100=>001111110
000001100=>010000010=>101111101=>110111110
000001101=>100000101=>011111010=>001111101
000001110=>100000110=>011111001=>101111100
000001111=>000001111=>111110000=>011111000
000010000=>000100000=>111011111=>111101111
000010001=>001000001=>110111110=>011011111
000010010=>101000000=>010111111=>101011111
000010011=>010000011=>101111100=>010111110
000010100=>011000000=>100111111=>110011111
000010101=>110000001=>001111110=>000111111
000010110=>110000010=>001111101=>100111110
000010111=>100000111=>011111000=>001111100
000011000=>001000010=>110111101=>111011110
000011001=>010000101=>101111010=>010111101
000011010=>110000100=>001111011=>100111101
000011011=>100001011=>011110100=>001111010
000011100=>010000110=>101111001=>110111100
000011101=>100001101=>011110010=>001111001
000011110=>100001110=>011110001=>101111000
000011111=>000011111=>111100000=>011110000
000100000=>000010000=>111101111=>111110111
000100001=>000100001=>111011110=>011101111
000100010=>100100000=>011011111=>101101111
000100011=>001000011=>110111100=>011011110
000100100=>010100000=>101011111=>110101111
000100101=>101000001=>010111110=>001011111
000100110=>101000010=>010111101=>101011110
000100111=>010000111=>101111000=>010111100
000101000=>001100000=>110011111=>111001111
000101001=>011000001=>100111110=>010011111
000101010=>111000000=>000111111=>100011111
000101011=>110000011=>001111100=>000111110
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1011110000=>0001101110=>1110010001=>1111001000
1100101010=>1110110000=>0001001111=>1000100111
1100110010=>1010110100=>0101001011=>1010100101
1101001010=>1101110000=>0010001111=>1001000111
1101010010=>1011110000=>0100001111=>1010000111
1110001010=>1100111000=>0011000111=>1001100011
1110010010=>1010111000=>0101000111=>1010100011
1110101000=>0011111000=>1100000111=>1110000011
1111000010=>1000111100=>0111000011=>1011100001
1111001000=>0010111100=>1101000011=>1110100001
1111010000=>0001111100=>1110000011=>1111000001
1111100000=>0000111110=>1111000001=>1111100000
101010101010=>111111000000=>000000111111=>100000011111
101010101100=>011111000010=>100000111101=>110000011110
101010110010=>101111000100=>010000111011=>101000011101
101011001010=>110111001000=>001000110111=>100100011011
101011001100=>010111001010=>101000110101=>110100011010
101011010010=>101111001000=>010000110111=>101000011011
101011010100=>011111001000=>100000110111=>110000011011
101011100100=>010111001100=>101000110011=>110100011001
101011110000=>000111001110=>111000110001=>111100011000
101100101010=>111011010000=>000100101111=>100010010111
101100110010=>101011010100=>010100101011=>101010010101
101101001010=>110111010000=>001000101111=>100100010111
101101010010=>101111010000=>010000101111=>101000010111
101101100010=>100111010100=>011000101011=>101100010101
101110001010=>110011011000=>001100100111=>100110010011
101110001100=>010011011010=>101100100101=>110110010010
101110010010=>101011011000=>010100100111=>101010010011
101110010100=>011011011000=>100100100111=>110010010011
101110100100=>010111011000=>101000100111=>110100010011
101110110000=>000111011010=>111000100101=>111100010010
101111000100=>010011011100=>101100100011=>110110010001
101111100000=>000011011110=>111100100001=>111110010000
110010101010=>111101100000=>000010011111=>100001001111
110010101100=>011101100010=>100010011101=>110001001110
110010110010=>101101100100=>010010011011=>101001001101
110011001010=>110101101000=>001010010111=>100101001011
110011001100=>010101101010=>101010010101=>110101001010
110011010010=>101101101000=>010010010111=>101001001011
110011010100=>011101101000=>100010010111=>110001001011
110011110000=>000101101110=>111010010001=>111101001000
110100101010=>111011100000=>000100011111=>100010001111
110100110010=>101011100100=>010100011011=>101010001101
110100110100=>011011100100=>100100011011=>110010001101
110101001010=>110111100000=>001000011111=>100100001111
110101001100=>010111100010=>101000011101=>110100001110
110101010010=>101111100000=>010000011111=>101000001111
110101010100=>011111100000=>100000011111=>110000001111
110101100100=>010111100100=>101000011011=>110100001101
110101110000=>000111100110=>111000011001=>111100001100
110110001010=>110011101000=>001100010111=>100110001011
110110010010=>101011101000=>010100010111=>101010001011
110110010100=>011011101000=>100100010111=>110010001011
110110100010=>100111101000=>011000010111=>101100001011
110110100100=>010111101000=>101000010111=>110100001011
110111000010=>100011101100=>011100010011=>101110001001
110111000100=>010011101100=>101100010011=>110110001001
110111100000=>000011101110=>111100010001=>111110001000
111000101010=>111001110000=>000110001111=>100011000111
111000101100=>011001110010=>100110001101=>110011000110
111001001010=>110101110000=>001010001111=>100101000111
111001010010=>101101110000=>010010001111=>101001000111
111001100010=>100101110100=>011010001011=>101101000101
111010001010=>110011110000=>001100001111=>100110000111
111010001100=>010011110010=>101100001101=>110110000110
111010010010=>101011110000=>010100001111=>101010000111
111010101000=>001111110000=>110000001111=>111000000111
111010110000=>000111110010=>111000001101=>111100000110
111100001100=>010001111010=>101110000101=>110111000010
111100010100=>011001111000=>100110000111=>110011000011
111100100100=>010101111000=>101010000111=>110101000011
111100110000=>000101111010=>111010000101=>111101000010
111101000010=>100011111000=>011100000111=>101110000011
111101000100=>010011111000=>101100000111=>110110000011
111101001000=>001011111000=>110100000111=>111010000011
111101010000=>000111111000=>111000000111=>111100000011
111110000010=>100001111100=>011110000011=>101111000001
111110001000=>001001111100=>110110000011=>111011000001
111110010000=>000101111100=>111010000011=>111101000001
111110100000=>000011111100=>111100000011=>111110000001
111111000000=>000001111110=>111110000001=>111111000000
1111111111=>1111111111=>0000000000=>0000000000
1111111110=>1111111110=>0000000001=>1000000000
1111111001=>0111111101=>1000000010=>0100000001
1111110000=>0001111110=>1110000001=>1111000000
1111100010=>1001111100=>0110000011=>1011000001
1111010100=>0111111000=>1000000111=>1100000011
1111010001=>0011111001=>1100000110=>0110000011
1110110001=>0011110101=>1100001010=>0110000101
1110101100=>0111110010=>1000001101=>1100000110
1110101001=>0111110001=>1000001110=>0100000111
1110011001=>0101110101=>1010001010=>0101000101
1110010101=>1101110001=>0010001110=>0001000111
1110010011=>0101110011=>1010001100=>0101000110
1110000001=>0000011101=>1111100010=>0111110001
1101111110=>1110111110=>0001000001=>1000100000
1101101001=>0111101001=>1000010110=>0100001011
1101010101=>1111100001=>0000011110=>0000001111
1100011110=>1001101110=>0110010001=>1011001000
1100000110=>1000011010=>0111100101=>1011110010
1100000000=>0000000110=>1111111001=>1111111100
1011111110=>1101111110=>0010000001=>1001000000
1011100000=>0000110110=>1111001001=>1111100100
1011011001=>0111010101=>1000101010=>0100010101
1011000001=>0000110101=>1111001010=>0111100101
1010110000=>0001110010=>1110001101=>1111000110
1010101000=>0011110000=>1100001111=>1110000111
1010011000=>0010110010=>1101001101=>1110100110
1010010010=>1010110000=>0101001111=>1010100111
1010001100=>0100110010=>1011001101=>1101100110
1001111110=>1010111110=>0101000001=>1010100000
1001110000=>0001010110=>1110101001=>1111010100
1001100111=>0101010111=>1010101000=>0101010100
1001100010=>1001010100=>0110101011=>1011010101
1001100001=>0001010101=>1110101010=>0111010101
1001010101=>1110100001=>0001011110=>0000101111
1001010010=>1011010000=>0100101111=>1010010111
1000111110=>1001011110=>0110100001=>1011010000
1000111000=>0010010110=>1101101001=>1110110100
1000101100=>0110010010=>1001101101=>1100110110
1000101010=>1110010000=>0001101111=>1000110111
1000011110=>1000101110=>0111010001=>1011101000
1000010101=>1100010001=>0011101110=>0001110111
1000001110=>1000010110=>0111101001=>1011110100
1000000111=>0000010111=>1111101000=>0111110100
1000000110=>1000001010=>0111110101=>1011111010
1000000010=>1000000100=>0111111011=>1011111101
10000000110=>10000001010=>01111110101=>10111111010
11111111110=>11111111110=>00000000001=>10000000000
0111111111=>0111111111=>1000000000=>0100000000
0111100001=>0001011101=>1110100010=>0111010001
0111000001=>0000101101=>1111010010=>0111101001
0000000001=>0000000001=>1111111110=>0111111111
01111111111=>01111111111=>10000000000=>01000000000
00000000001=>00000000001=>11111111110=>01111111111
0101010101=>1111000001=>0000111110=>0000011111
0101000111=>0011000111=>1100111000=>0110011100
0100110011=>0101001011=>1010110100=>0101011010
0100100111=>0101000111=>1010111000=>0101011100
0100001111=>0001001111=>1110110000=>0111011000
0011000111=>0010010111=>1101101000=>0110110100
0010101011=>1110000011=>0001111100=>0000111110
0010001111=>0010001111=>1101110000=>0110111000
0001110011=>0100011011=>1011100100=>0101110010
0001100111=>0100010111=>1011101000=>0101110100
0001011011=>1100001011=>0011110100=>0001111010
0001010111=>1100000111=>0011111000=>0001111100
0001001111=>0100001111=>1011110000=>0101111000
0000111011=>1000011011=>0111100100=>0011110010
0000110111=>1000010111=>0111101000=>0011110100
0000101111=>1000001111=>0111110000=>0011111000
0000011111=>0000011111=>1111100000=>0111110000
010101000111=>001110000111=>110001111000=>011000111100
010100001111=>000110001111=>111001110000=>011100111000
010011001011=>101010010011=>010101101100=>001010110110
010011000111=>001010010111=>110101101000=>011010110100
010010001111=>001010001111=>110101110000=>011010111000
010001110011=>010010011011=>101101100100=>010110110010
010001100111=>010010010111=>101101101000=>010110110100
010001001111=>010010001111=>101101110000=>010110111000
010000111011=>100010011011=>011101100100=>001110110010
010000110111=>100010010111=>011101101000=>001110110100
010000101111=>100010001111=>011101110000=>001110111000
010000011111=>000010011111=>111101100000=>011110110000
001101001011=>101100100011=>010011011100=>001001101110
001101000111=>001100100111=>110011011000=>011001101100
001100110011=>010100101011=>101011010100=>010101101010
001100100111=>010100100111=>101011011000=>010101101100
001100011011=>100100101011=>011011010100=>001101101010
001100001111=>000100101111=>111011010000=>011101101000
001011000111=>001100010111=>110011101000=>011001110100
001010101011=>111100000011=>000011111100=>000001111110
001010001111=>001100001111=>110011110000=>011001111000
001001110011=>010100011011=>101011100100=>010101110010
001001100111=>010100010111=>101011101000=>010101110100
001001001111=>010100001111=>101011110000=>010101111000
001000011111=>000100011111=>111011100000=>011101110000
000111000111=>001000110111=>110111001000=>011011100100
000110101011=>111000100011=>000111011100=>000011101110
000110001111=>001000101111=>110111010000=>011011101000
000101011011=>111000001011=>000111110100=>000011111010
000101010111=>111000000111=>000111111000=>000011111100
000100011111=>001000011111=>110111100000=>011011110000
000011110011=>010000111011=>101111000100=>010111100010
000011101011=>110000110011=>001111001100=>000111100110
000011100111=>010000110111=>101111001000=>010111100100
000011011011=>110000101011=>001111010100=>000111101010
000011010111=>110000100111=>001111011000=>000111101100
000011001111=>010000101111=>101111010000=>010111101000
000010111011=>110000011011=>001111100100=>000111110010
000010110111=>110000010111=>001111101000=>000111110100
000010101111=>110000001111=>001111110000=>000111111000
000010011111=>010000011111=>101111100000=>010111110000
000001111011=>100000111011=>011111000100=>001111100010
000001110111=>100000110111=>011111001000=>001111100100
000001101111=>100000101111=>011111010000=>001111101000
000001011111=>100000011111=>011111100000=>001111110000
000000111111=>000000111111=>111111000000=>011111100000
111111111111=>111111111111=>000000000000=>000000000000
111110000001=>000001111101=>111110000010=>011111000001
111001100001=>000101110101=>111010001010=>011101000101
111000011001=>010001110101=>101110001010=>010111000101
111000000111=>000001110111=>111110001000=>011111000100
111000110001=>001001110101=>110110001010=>011011000101
111011000001=>000011110101=>111100001010=>011110000101
100111100001=>000101011101=>111010100010=>011101010001
100110011001=>010101010101=>101010101010=>010101010101
100110000111=>000101010111=>111010101000=>011101010100
100110110001=>001101010101=>110010101010=>011001010101
100001111001=>010001011101=>101110100010=>010111010001
100001100111=>010001010111=>101110101000=>010111010100
100000011111=>000001011111=>111110100000=>011111010000
100000110111=>100001010111=>011110101000=>001111010100
100011000111=>001001010111=>110110101000=>011011010100
100011110001=>001001011101=>110110100010=>011011010001
101101100001=>000111010101=>111000101010=>011100010101
101100011001=>010011010101=>101100101010=>010110010101
101100000111=>000011010111=>111100101000=>011110010100
101100110001=>001011010101=>110100101010=>011010010101
101111000001=>000011011101=>111100100010=>011110010001
101001000111=>001011000111=>110100111000=>011010011100
101001110001=>001011001101=>110100110010=>011010011001
0000000000=>0000000000=>1111111111=>1111111111
0000011110=>1000001110=>0111110001=>1011111000
0001111110=>1000111110=>0111000001=>1011100000
0111111110=>1011111110=>0100000001=>1010000000
0100111110=>1010011110=>0101100001=>1010110000
000000000000=>000000000000=>111111111111=>111111111111
0101010100=>0111100000=>1000011111=>1100001111
0000010100=>0110000000=>1001111111=>1100111111
0000000010=>1000000000=>0111111111=>1011111111
0000001110=>1000000110=>0111111001=>1011111100
0000111110=>1000011110=>0111100001=>1011110000
0011111110=>1001111110=>0110000001=>1011000000
00000000010=>10000000000=>01111111111=>10111111111
00000001110=>10000000110=>01111111001=>10111111100
00000111110=>10000011110=>01111100001=>10111110000
0001011110=>1100001110=>0011110001=>1001111000
00011111110=>10001111110=>01110000001=>10111000000
01111111110=>10111111110=>01000000001=>10100000000
0011100010=>1001001100=>0110110011=>1011011001
0011110000=>0001001110=>1110110001=>1111011000
0110001100=>0100101010=>1011010101=>1101101010
0110100100=>0101101000=>1010010111=>1101001011
0110110000=>0001101010=>1110010101=>1111001010
001011011000=>001110001010=>110001110101=>111000111010
001011100100=>010110001100=>101001110011=>110100111001
001011101000=>001110001100=>110001110011=>111000111001
001011110000=>000110001110=>111001110001=>111100111000
001100111000=>001010010110=>110101101001=>111010110100
001101110000=>000110010110=>111001101001=>111100110100
001110010100=>011010011000=>100101100111=>110010110011
001110011000=>001010011010=>110101100101=>111010110010
001110100100=>010110011000=>101001100111=>110100110011
001110110000=>000110011010=>111001100101=>111100110010
001111000010=>100010011100=>011101100011=>101110110001
001111000100=>010010011100=>101101100011=>110110110001
001111001000=>001010011100=>110101100011=>111010110001
001111010000=>000110011100=>111001100011=>111100110001
001111100000=>000010011110=>111101100001=>111110110000
010011110000=>000101001110=>111010110001=>111101011000
010100110100=>011011000100=>100100111011=>110010011101
010100111000=>001011000110=>110100111001=>111010011100
010101011000=>001111000010=>110000111101=>111000011110
010101100100=>010111000100=>101000111011=>110100011101
010101110000=>000111000110=>111000111001=>111100011100
010110010100=>011011001000=>100100110111=>110010011011
010110011000=>001011001010=>110100110101=>111010011010
010110100100=>010111001000=>101000110111=>110100011011
010110110000=>000111001010=>111000110101=>111100011010
010111000010=>100011001100=>011100110011=>101110011001
010111000100=>010011001100=>101100110011=>110110011001
010111001000=>001011001100=>110100110011=>111010011001
010111010000=>000111001100=>111000110011=>111100011001
010111100000=>000011001110=>111100110001=>111110011000
011000111000=>001001010110=>110110101001=>111011010100
011001110000=>000101010110=>111010101001=>111101010100
011010010100=>011011010000=>100100101111=>110010010111
011010100100=>010111010000=>101000101111=>110100010111
011011100000=>000011010110=>111100101001=>111110010100
011100010100=>011001011000=>100110100111=>110011010011
011100011000=>001001011010=>110110100101=>111011010010
011100110000=>000101011010=>111010100101=>111101010010
011101000100=>010011011000=>101100100111=>110110010011
011101100000=>000011011010=>111100100101=>111110010010
011110000010=>100001011100=>011110100011=>101111010001
011110000100=>010001011100=>101110100011=>110111010001
011110001000=>001001011100=>110110100011=>111011010001
011110010000=>000101011100=>111010100011=>111101010001
011110100000=>000011011100=>111100100011=>111110010001
011111000000=>000001011110=>111110100001=>111111010000
10101010101=>11111000001=>00000111110=>00000011111
0101110001=>0011001101=>1100110010=>0110011001
0110011001=>0101010101=>1010101010=>0101010101
0110110001=>0011010101=>1100101010=>0110010101
011100011001=>010010110101=>101101001010=>010110100101
011101001100=>010110110010=>101001001101=>110100100110
011101100001=>000110110101=>111001001010=>011100100101
0100000100=>0100001000=>1011110111=>1101111011
0000000101=>1000000001=>0111111110=>0011111111
100101110001=>001101001101=>110010110010=>011001011001
101011100001=>000111001101=>111000110010=>011100011001
0011000110=>1001001010=>0110110101=>1011011010
0010001110=>1001000110=>0110111001=>1011011100
0110111001=>0110101101=>1001010010=>0100101001
0000010001=>0010000001=>1101111110=>0110111111
101000111001=>010011001101=>101100110010=>010110011001
100100111001=>010101001101=>101010110010=>010101011001
100110100011=>001101010011=>110010101100=>011001010110
101001100011=>001011001011=>110100110100=>011010011010
100101100011=>001101001011=>110010110100=>011001011010
100110010011=>010101010011=>101010101100=>010101010110
101000110011=>010011001011=>101100110100=>010110011010
100100110011=>010101001011=>101010110100=>010101011010
101010000111=>000111000111=>111000111000=>011100011100
100101000111=>001101000111=>110010111000=>011001011100
101000100111=>010011000111=>101100111000=>010110011100
100100100111=>010101000111=>101010111000=>010101011100
0110010011=>0101010011=>1010101100=>0101010110
011100010011=>010010110011=>101101001100=>010110100110
011010001011=>100110100011=>011001011100=>001100101110
101100100011=>001011010011=>110100101100=>011010010110
101100010011=>010011010011=>101100101100=>010110010110
011100000111=>000010110111=>111101001000=>011110100100
0101000000=>0000011000=>1111100111=>1111110011
110011001101=>101011010101=>010100101010=>001010010101
110100011101=>100111001101=>011000110010=>001100011001
110000111101=>100011011101=>011100100010=>001110010001
101100011011=>100110101011=>011001010100=>001100101010
100110011011=>101010101011=>010101010100=>001010101010
101000111011=>100110011011=>011001100100=>001100110010
100100111011=>101010011011=>010101100100=>001010110010
101100010111=>100110100111=>011001011000=>001100101100
100110010111=>101010100111=>010101011000=>001010101100
101000110111=>100110010111=>011001101000=>001100110100
100100110111=>101010010111=>010101101000=>001010110100
101000101111=>100110001111=>011001110000=>001100111000
100100101111=>101010001111=>010101110000=>001010111000
0011111111=>0011111111=>1100000000=>0110000000
00111111111=>00111111111=>11000000000=>01100000000
0011111100=>0100111110=>1011000001=>1101100000
0011111001=>0100111101=>1011000010=>0101100001
0011110011=>0100111011=>1011000100=>0101100010
0110100111=>0110100111=>1001011000=>0100101100
0110110011=>0110101011=>1001010100=>0100101010
0100101001=>0110100001=>1001011110=>0100101111
101011000011=>000111001011=>111000110100=>011100011010
101101000011=>000111010011=>111000101100=>011100010110
0100010101=>1100100001=>0011011110=>0001101111
0001010101=>1110000001=>0001111110=>0000111111
0000110101=>1100001001=>0011110110=>0001111011
0011110101=>1100111001=>0011000110=>0001100011
0110000011=>0000101011=>1111010100=>0111101010
0110011011=>1010101011=>0101010100=>0010101010
110110001101=>100111010101=>011000101010=>001100010101
111100001101=>100011110101=>011100001010=>001110000101
000011111101=>100001111101=>011110000010=>001111000001
001111001101=>101001110101=>010110001010=>001011000101
011110001101=>100101110101=>011010001010=>001101000101
0100111001=>0101001101=>1010110010=>0101011001
0101100011=>0011001011=>1100110100=>0110011010
011001000111=>001010100111=>110101011000=>011010101100
011101000011=>000110110011=>111001001100=>011100100110
0111011001=>0110110101=>1001001010=>0100100101
0101111001=>0110011101=>1001100010=>0100110001
0101110011=>0110011011=>1001100100=>0100110010
0110100011=>0011010011=>1100101100=>0110010110
0101100111=>0110010111=>1001101000=>0100110100
0101001111=>0110001111=>1001110000=>0100111000
101100101111=>101101001111=>010010110000=>001001011000
0001010000=>0001100000=>1110011111=>1111001111
0001000100=>0100100000=>1011011111=>1101101111
0111010011=>0110110011=>1001001100=>0100100110
010100000000=>000000011000=>111111100111=>111111110011
000101000000=>000001100000=>111110011111=>111111001111
010001000000=>000001001000=>111110110111=>111111011011
000001010000=>000110000000=>111001111111=>111100111111
010101010000=>000111100000=>111000011111=>111100001111
000100010000=>000100100000=>111011011111=>111101101111
011010010000=>000101101000=>111010010111=>111101001011
000000010100=>011000000000=>100111111111=>110011111111
010100010100=>011001100000=>100110011111=>110011001111
000101010100=>011110000000=>100001111111=>110000111111
000100000100=>010000100000=>101111011111=>110111101111
011010000100=>010001101000=>101110010111=>110111001011
000110100100=>010110001000=>101001110111=>110100111011
011000100100=>010100101000=>101011010111=>110101101011
011100011101=>100101101101=>011010010010=>001101001001
111000011101=>100011101101=>011100010010=>001110001001
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
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
This is the word obtained by moving the last letter to the beginnig.
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