- FindStat

Identifier

Mp00104: Binary words —reverse⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words

Images

0 => 0 => 0 => 0

1 => 1 => 1 => 1

00 => 00 => 00 => 00

01 => 10 => 01 => 01

10 => 01 => 10 => 10

11 => 11 => 11 => 11

000 => 000 => 000 => 000

001 => 100 => 001 => 001

010 => 010 => 100 => 010

011 => 110 => 101 => 101

100 => 001 => 010 => 100

101 => 101 => 011 => 011

110 => 011 => 110 => 110

111 => 111 => 111 => 111

0000 => 0000 => 0000 => 0000

0001 => 1000 => 0001 => 0001

0010 => 0100 => 1000 => 0010

0011 => 1100 => 1001 => 0101

0100 => 0010 => 0100 => 0100

0101 => 1010 => 0101 => 1001

0110 => 0110 => 1100 => 1010

0111 => 1110 => 1101 => 1101

1000 => 0001 => 0010 => 1000

1001 => 1001 => 0011 => 0011

1010 => 0101 => 1010 => 0110

1011 => 1101 => 1011 => 1011

1100 => 0011 => 0110 => 1100

1101 => 1011 => 0111 => 0111

1110 => 0111 => 1110 => 1110

1111 => 1111 => 1111 => 1111

00000 => 00000 => 00000 => 00000

00001 => 10000 => 00001 => 00001

00010 => 01000 => 10000 => 00010

00011 => 11000 => 10001 => 00101

00100 => 00100 => 01000 => 00100

00101 => 10100 => 01001 => 01001

00110 => 01100 => 11000 => 01010

00111 => 11100 => 11001 => 10101

01000 => 00010 => 00100 => 01000

01001 => 10010 => 00101 => 10001

01010 => 01010 => 10100 => 10010

01011 => 11010 => 10101 => 01101

01100 => 00110 => 01100 => 10100

01101 => 10110 => 01101 => 11001

01110 => 01110 => 11100 => 11010

01111 => 11110 => 11101 => 11101

10000 => 00001 => 00010 => 10000

10001 => 10001 => 00011 => 00011

10010 => 01001 => 10010 => 00110

10011 => 11001 => 10011 => 01011

10100 => 00101 => 01010 => 01100

10101 => 10101 => 01011 => 10011

10110 => 01101 => 11010 => 10110

10111 => 11101 => 11011 => 11011

11000 => 00011 => 00110 => 11000

11001 => 10011 => 00111 => 00111

11010 => 01011 => 10110 => 01110

11011 => 11011 => 10111 => 10111

11100 => 00111 => 01110 => 11100

11101 => 10111 => 01111 => 01111

11110 => 01111 => 11110 => 11110

11111 => 11111 => 11111 => 11111

000000 => 000000 => 000000 => 000000

000001 => 100000 => 000001 => 000001

000010 => 010000 => 100000 => 000010

000011 => 110000 => 100001 => 000101

000100 => 001000 => 010000 => 000100

000101 => 101000 => 010001 => 001001

000110 => 011000 => 110000 => 001010

000111 => 111000 => 110001 => 010101

001000 => 000100 => 001000 => 001000

001001 => 100100 => 001001 => 010001

001010 => 010100 => 101000 => 010010

001011 => 110100 => 101001 => 100101

001100 => 001100 => 011000 => 010100

001101 => 101100 => 011001 => 101001

001110 => 011100 => 111000 => 101010

001111 => 111100 => 111001 => 110101

010000 => 000010 => 000100 => 010000

010001 => 100010 => 000101 => 100001

010010 => 010010 => 100100 => 100010

010011 => 110010 => 100101 => 001101

010100 => 001010 => 010100 => 100100

010101 => 101010 => 010101 => 011001

010110 => 011010 => 110100 => 011010

010111 => 111010 => 110101 => 101101

011000 => 000110 => 001100 => 101000

011001 => 100110 => 001101 => 110001

011010 => 010110 => 101100 => 110010

011011 => 110110 => 101101 => 011101

011100 => 001110 => 011100 => 110100

011101 => 101110 => 011101 => 111001

011110 => 011110 => 111100 => 111010

011111 => 111110 => 111101 => 111101

100000 => 000001 => 000010 => 100000

100001 => 100001 => 000011 => 000011

100010 => 010001 => 100010 => 000110

100011 => 110001 => 100011 => 001011

100100 => 001001 => 010010 => 001100

100101 => 101001 => 010011 => 010011

100110 => 011001 => 110010 => 010110

>>> Load all 1049 entries. <<<

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.

Map

inverse Foata bijection

Description

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