- FindStat

Identifier

Mp00200: Binary words —twist⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00268: Binary words —zeros to flag zeros⟶ Binary words

Images

0 => 1 => 1 => 1

1 => 0 => 0 => 0

00 => 10 => 01 => 00

01 => 11 => 11 => 11

10 => 00 => 00 => 10

11 => 01 => 10 => 01

000 => 100 => 001 => 110

001 => 101 => 101 => 001

010 => 110 => 011 => 000

011 => 111 => 111 => 111

100 => 000 => 000 => 010

101 => 001 => 100 => 101

110 => 010 => 010 => 100

111 => 011 => 110 => 011

0000 => 1000 => 0001 => 0010

0001 => 1001 => 1001 => 1101

0010 => 1010 => 0101 => 1100

0011 => 1011 => 1101 => 0011

0100 => 1100 => 0011 => 1110

0101 => 1101 => 1011 => 0001

0110 => 1110 => 0111 => 0000

0111 => 1111 => 1111 => 1111

1000 => 0000 => 0000 => 1010

1001 => 0001 => 1000 => 0101

1010 => 0010 => 0100 => 0100

1011 => 0011 => 1100 => 1011

1100 => 0100 => 0010 => 0110

1101 => 0101 => 1010 => 1001

1110 => 0110 => 0110 => 1000

1111 => 0111 => 1110 => 0111

00000 => 10000 => 00001 => 11010

00001 => 10001 => 10001 => 00101

00010 => 10010 => 01001 => 00100

00011 => 10011 => 11001 => 11011

00100 => 10100 => 00101 => 00110

00101 => 10101 => 10101 => 11001

00110 => 10110 => 01101 => 11000

00111 => 10111 => 11101 => 00111

01000 => 11000 => 00011 => 00010

01001 => 11001 => 10011 => 11101

01010 => 11010 => 01011 => 11100

01011 => 11011 => 11011 => 00011

01100 => 11100 => 00111 => 11110

01101 => 11101 => 10111 => 00001

01110 => 11110 => 01111 => 00000

01111 => 11111 => 11111 => 11111

10000 => 00000 => 00000 => 01010

10001 => 00001 => 10000 => 10101

10010 => 00010 => 01000 => 10100

10011 => 00011 => 11000 => 01011

10100 => 00100 => 00100 => 10110

10101 => 00101 => 10100 => 01001

10110 => 00110 => 01100 => 01000

10111 => 00111 => 11100 => 10111

11000 => 01000 => 00010 => 10010

11001 => 01001 => 10010 => 01101

11010 => 01010 => 01010 => 01100

11011 => 01011 => 11010 => 10011

11100 => 01100 => 00110 => 01110

11101 => 01101 => 10110 => 10001

11110 => 01110 => 01110 => 10000

11111 => 01111 => 11110 => 01111

000000 => 100000 => 000001 => 001010

000001 => 100001 => 100001 => 110101

000010 => 100010 => 010001 => 110100

000011 => 100011 => 110001 => 001011

000100 => 100100 => 001001 => 110110

000101 => 100101 => 101001 => 001001

000110 => 100110 => 011001 => 001000

000111 => 100111 => 111001 => 110111

001000 => 101000 => 000101 => 110010

001001 => 101001 => 100101 => 001101

001010 => 101010 => 010101 => 001100

001011 => 101011 => 110101 => 110011

001100 => 101100 => 001101 => 001110

001101 => 101101 => 101101 => 110001

001110 => 101110 => 011101 => 110000

001111 => 101111 => 111101 => 001111

010000 => 110000 => 000011 => 111010

010001 => 110001 => 100011 => 000101

010010 => 110010 => 010011 => 000100

010011 => 110011 => 110011 => 111011

010100 => 110100 => 001011 => 000110

010101 => 110101 => 101011 => 111001

010110 => 110110 => 011011 => 111000

010111 => 110111 => 111011 => 000111

011000 => 111000 => 000111 => 000010

011001 => 111001 => 100111 => 111101

011010 => 111010 => 010111 => 111100

011011 => 111011 => 110111 => 000011

011100 => 111100 => 001111 => 111110

011101 => 111101 => 101111 => 000001

011110 => 111110 => 011111 => 000000

011111 => 111111 => 111111 => 111111

100000 => 000000 => 000000 => 101010

100001 => 000001 => 100000 => 010101

100010 => 000010 => 010000 => 010100

100011 => 000011 => 110000 => 101011

100100 => 000100 => 001000 => 010110

100101 => 000101 => 101000 => 101001

100110 => 000110 => 011000 => 101000

>>> Load all 1632 entries. <<<

Map

twist

Description

Return the binary word with first letter inverted.

Map

reverse

Description

Return the reversal of a binary word.

Map

zeros to flag zeros

Description

Return a binary word of the same length, such that the number of occurrences of $10$ in the word obtained by prepending the reverse of the complement equals the number of $0$s in the original word.
For example, the image of the word $w=1\dots1$ is $1\dots1$, because $w$ has no zeros, and $1\dots1$ is the only word such that prepending the reverse of its complement has no occurrence of the factor $10$.
On the other hand, $0\dots0$ must be mapped to $10\dots10$ if the length is even, and $010\dots10$ if it is odd.