- FindStat

Identifier

Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words

Images

0 => 0 => 0 => 1

1 => 1 => 1 => 0

00 => 00 => 00 => 11

01 => 10 => 10 => 01

10 => 01 => 01 => 10

11 => 11 => 11 => 00

000 => 000 => 000 => 111

001 => 010 => 100 => 011

010 => 100 => 010 => 101

011 => 110 => 110 => 001

100 => 001 => 001 => 110

101 => 011 => 011 => 100

110 => 101 => 101 => 010

111 => 111 => 111 => 000

0000 => 0000 => 0000 => 1111

0001 => 0010 => 1000 => 0111

0010 => 0100 => 0100 => 1011

0011 => 0110 => 1100 => 0011

0100 => 1000 => 0010 => 1101

0101 => 1010 => 0110 => 1001

0110 => 1100 => 1010 => 0101

0111 => 1110 => 1110 => 0001

1000 => 0001 => 0001 => 1110

1001 => 0011 => 0011 => 1100

1010 => 0101 => 1001 => 0110

1011 => 0111 => 0111 => 1000

1100 => 1001 => 0101 => 1010

1101 => 1011 => 1011 => 0100

1110 => 1101 => 1101 => 0010

1111 => 1111 => 1111 => 0000

00000 => 00000 => 00000 => 11111

00001 => 00010 => 10000 => 01111

00010 => 00100 => 01000 => 10111

00011 => 00110 => 11000 => 00111

00100 => 01000 => 00100 => 11011

00101 => 01010 => 01100 => 10011

00110 => 01100 => 10100 => 01011

00111 => 01110 => 11100 => 00011

01000 => 10000 => 00010 => 11101

01001 => 10010 => 00110 => 11001

01010 => 10100 => 10010 => 01101

01011 => 10110 => 01110 => 10001

01100 => 11000 => 01010 => 10101

01101 => 11010 => 10110 => 01001

01110 => 11100 => 11010 => 00101

01111 => 11110 => 11110 => 00001

10000 => 00001 => 00001 => 11110

10001 => 00011 => 00011 => 11100

10010 => 00101 => 10001 => 01110

10011 => 00111 => 00111 => 11000

10100 => 01001 => 01001 => 10110

10101 => 01011 => 10011 => 01100

10110 => 01101 => 11001 => 00110

10111 => 01111 => 01111 => 10000

11000 => 10001 => 00101 => 11010

11001 => 10011 => 01011 => 10100

11010 => 10101 => 01101 => 10010

11011 => 10111 => 10111 => 01000

11100 => 11001 => 10101 => 01010

11101 => 11011 => 11011 => 00100

11110 => 11101 => 11101 => 00010

11111 => 11111 => 11111 => 00000

000000 => 000000 => 000000 => 111111

000001 => 000010 => 100000 => 011111

000010 => 000100 => 010000 => 101111

000011 => 000110 => 110000 => 001111

000100 => 001000 => 001000 => 110111

000101 => 001010 => 011000 => 100111

000110 => 001100 => 101000 => 010111

000111 => 001110 => 111000 => 000111

001000 => 010000 => 000100 => 111011

001001 => 010010 => 001100 => 110011

001010 => 010100 => 100100 => 011011

001011 => 010110 => 011100 => 100011

001100 => 011000 => 010100 => 101011

001101 => 011010 => 101100 => 010011

001110 => 011100 => 110100 => 001011

001111 => 011110 => 111100 => 000011

010000 => 100000 => 000010 => 111101

010001 => 100010 => 000110 => 111001

010010 => 100100 => 100010 => 011101

010011 => 100110 => 001110 => 110001

010100 => 101000 => 010010 => 101101

010101 => 101010 => 100110 => 011001

010110 => 101100 => 110010 => 001101

010111 => 101110 => 011110 => 100001

011000 => 110000 => 001010 => 110101

011001 => 110010 => 010110 => 101001

011010 => 110100 => 011010 => 100101

011011 => 110110 => 101110 => 010001

011100 => 111000 => 101010 => 010101

011101 => 111010 => 110110 => 001001

011110 => 111100 => 111010 => 000101

011111 => 111110 => 111110 => 000001

100000 => 000001 => 000001 => 111110

100001 => 000011 => 000011 => 111100

100010 => 000101 => 100001 => 011110

100011 => 000111 => 000111 => 111000

100100 => 001001 => 010001 => 101110

100101 => 001011 => 100011 => 011100

100110 => 001101 => 110001 => 001110

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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.

Map

complement

Description

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