- FindStat

Identifier

Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words

Images

0 => 0 => 1 => 1

1 => 1 => 0 => 0

00 => 00 => 11 => 11

01 => 10 => 01 => 01

10 => 01 => 10 => 10

11 => 11 => 00 => 00

000 => 000 => 111 => 111

001 => 100 => 011 => 011

010 => 010 => 101 => 101

011 => 110 => 001 => 001

100 => 001 => 110 => 110

101 => 101 => 010 => 100

110 => 011 => 100 => 010

111 => 111 => 000 => 000

0000 => 0000 => 1111 => 1111

0001 => 1000 => 0111 => 0111

0010 => 0100 => 1011 => 1011

0011 => 1100 => 0011 => 0011

0100 => 0010 => 1101 => 1101

0101 => 1010 => 0101 => 1001

0110 => 0110 => 1001 => 0101

0111 => 1110 => 0001 => 0001

1000 => 0001 => 1110 => 1110

1001 => 1001 => 0110 => 1100

1010 => 0101 => 1010 => 0110

1011 => 1101 => 0010 => 1000

1100 => 0011 => 1100 => 1010

1101 => 1011 => 0100 => 0100

1110 => 0111 => 1000 => 0010

1111 => 1111 => 0000 => 0000

00000 => 00000 => 11111 => 11111

00001 => 10000 => 01111 => 01111

00010 => 01000 => 10111 => 10111

00011 => 11000 => 00111 => 00111

00100 => 00100 => 11011 => 11011

00101 => 10100 => 01011 => 10011

00110 => 01100 => 10011 => 01011

00111 => 11100 => 00011 => 00011

01000 => 00010 => 11101 => 11101

01001 => 10010 => 01101 => 11001

01010 => 01010 => 10101 => 01101

01011 => 11010 => 00101 => 10001

01100 => 00110 => 11001 => 10101

01101 => 10110 => 01001 => 01001

01110 => 01110 => 10001 => 00101

01111 => 11110 => 00001 => 00001

10000 => 00001 => 11110 => 11110

10001 => 10001 => 01110 => 11100

10010 => 01001 => 10110 => 01110

10011 => 11001 => 00110 => 11000

10100 => 00101 => 11010 => 10110

10101 => 10101 => 01010 => 01100

10110 => 01101 => 10010 => 00110

10111 => 11101 => 00010 => 10000

11000 => 00011 => 11100 => 11010

11001 => 10011 => 01100 => 10100

11010 => 01011 => 10100 => 10010

11011 => 11011 => 00100 => 01000

11100 => 00111 => 11000 => 01010

11101 => 10111 => 01000 => 00100

11110 => 01111 => 10000 => 00010

11111 => 11111 => 00000 => 00000

000000 => 000000 => 111111 => 111111

000001 => 100000 => 011111 => 011111

000010 => 010000 => 101111 => 101111

000011 => 110000 => 001111 => 001111

000100 => 001000 => 110111 => 110111

000101 => 101000 => 010111 => 100111

000110 => 011000 => 100111 => 010111

000111 => 111000 => 000111 => 000111

001000 => 000100 => 111011 => 111011

001001 => 100100 => 011011 => 110011

001010 => 010100 => 101011 => 011011

001011 => 110100 => 001011 => 100011

001100 => 001100 => 110011 => 101011

001101 => 101100 => 010011 => 010011

001110 => 011100 => 100011 => 001011

001111 => 111100 => 000011 => 000011

010000 => 000010 => 111101 => 111101

010001 => 100010 => 011101 => 111001

010010 => 010010 => 101101 => 011101

010011 => 110010 => 001101 => 110001

010100 => 001010 => 110101 => 101101

010101 => 101010 => 010101 => 011001

010110 => 011010 => 100101 => 001101

010111 => 111010 => 000101 => 100001

011000 => 000110 => 111001 => 110101

011001 => 100110 => 011001 => 101001

011010 => 010110 => 101001 => 100101

011011 => 110110 => 001001 => 010001

011100 => 001110 => 110001 => 010101

011101 => 101110 => 010001 => 001001

011110 => 011110 => 100001 => 000101

011111 => 111110 => 000001 => 000001

100000 => 000001 => 111110 => 111110

100001 => 100001 => 011110 => 111100

100010 => 010001 => 101110 => 011110

100011 => 110001 => 001110 => 111000

100100 => 001001 => 110110 => 101110

100101 => 101001 => 010110 => 011100

100110 => 011001 => 100110 => 001110

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Map

reverse

Description

Return the reversal of a binary word.

Map

complement

Description

Send a binary word to the word obtained by interchanging the two letters.

Map

inverse Foata bijection

Description

The inverse of Foata's bijection.
See Mp00096Foata bijection.