- FindStat

Identifier

Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00200: Binary words —twist⟶ Binary words

Images

0 => 0 => 1

1 => 1 => 0

00 => 01 => 11

01 => 00 => 10

10 => 11 => 01

11 => 10 => 00

000 => 010 => 110

001 => 011 => 111

010 => 000 => 100

011 => 001 => 101

100 => 110 => 010

101 => 111 => 011

110 => 100 => 000

111 => 101 => 001

0000 => 0101 => 1101

0001 => 0100 => 1100

0010 => 0111 => 1111

0011 => 0110 => 1110

0100 => 0001 => 1001

0101 => 0000 => 1000

0110 => 0011 => 1011

0111 => 0010 => 1010

1000 => 1101 => 0101

1001 => 1100 => 0100

1010 => 1111 => 0111

1011 => 1110 => 0110

1100 => 1001 => 0001

1101 => 1000 => 0000

1110 => 1011 => 0011

1111 => 1010 => 0010

00000 => 01010 => 11010

00001 => 01011 => 11011

00010 => 01000 => 11000

00011 => 01001 => 11001

00100 => 01110 => 11110

00101 => 01111 => 11111

00110 => 01100 => 11100

00111 => 01101 => 11101

01000 => 00010 => 10010

01001 => 00011 => 10011

01010 => 00000 => 10000

01011 => 00001 => 10001

01100 => 00110 => 10110

01101 => 00111 => 10111

01110 => 00100 => 10100

01111 => 00101 => 10101

10000 => 11010 => 01010

10001 => 11011 => 01011

10010 => 11000 => 01000

10011 => 11001 => 01001

10100 => 11110 => 01110

10101 => 11111 => 01111

10110 => 11100 => 01100

10111 => 11101 => 01101

11000 => 10010 => 00010

11001 => 10011 => 00011

11010 => 10000 => 00000

11011 => 10001 => 00001

11100 => 10110 => 00110

11101 => 10111 => 00111

11110 => 10100 => 00100

11111 => 10101 => 00101

000000 => 010101 => 110101

000001 => 010100 => 110100

000010 => 010111 => 110111

000011 => 010110 => 110110

000100 => 010001 => 110001

000101 => 010000 => 110000

000110 => 010011 => 110011

000111 => 010010 => 110010

001000 => 011101 => 111101

001001 => 011100 => 111100

001010 => 011111 => 111111

001011 => 011110 => 111110

001100 => 011001 => 111001

001101 => 011000 => 111000

001110 => 011011 => 111011

001111 => 011010 => 111010

010000 => 000101 => 100101

010001 => 000100 => 100100

010010 => 000111 => 100111

010011 => 000110 => 100110

010100 => 000001 => 100001

010101 => 000000 => 100000

010110 => 000011 => 100011

010111 => 000010 => 100010

011000 => 001101 => 101101

011001 => 001100 => 101100

011010 => 001111 => 101111

011011 => 001110 => 101110

011100 => 001001 => 101001

011101 => 001000 => 101000

011110 => 001011 => 101011

011111 => 001010 => 101010

100000 => 110101 => 010101

100001 => 110100 => 010100

100010 => 110111 => 010111

100011 => 110110 => 010110

100100 => 110001 => 010001

100101 => 110000 => 010000

100110 => 110011 => 010011

>>> Load all 3710 entries. <<<

Map

alternating inverse

Description

Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.

Map

twist

Description

Return the binary word with first letter inverted.