- FindStat

Identifier

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

Images

0 => 1 => 1 => 1

1 => 0 => 0 => 0

00 => 11 => 11 => 11

01 => 10 => 01 => 01

10 => 01 => 10 => 10

11 => 00 => 00 => 00

000 => 111 => 111 => 111

001 => 110 => 101 => 101

010 => 101 => 011 => 011

011 => 100 => 001 => 001

100 => 011 => 110 => 110

101 => 010 => 100 => 010

110 => 001 => 010 => 100

111 => 000 => 000 => 000

0000 => 1111 => 1111 => 1111

0001 => 1110 => 1101 => 1101

0010 => 1101 => 1011 => 1011

0011 => 1100 => 1001 => 0101

0100 => 1011 => 0111 => 0111

0101 => 1010 => 0101 => 1001

0110 => 1001 => 0011 => 0011

0111 => 1000 => 0001 => 0001

1000 => 0111 => 1110 => 1110

1001 => 0110 => 1100 => 1010

1010 => 0101 => 1010 => 0110

1011 => 0100 => 1000 => 0010

1100 => 0011 => 0110 => 1100

1101 => 0010 => 0100 => 0100

1110 => 0001 => 0010 => 1000

1111 => 0000 => 0000 => 0000

00000 => 11111 => 11111 => 11111

00001 => 11110 => 11101 => 11101

00010 => 11101 => 11011 => 11011

00011 => 11100 => 11001 => 10101

00100 => 11011 => 10111 => 10111

00101 => 11010 => 10101 => 01101

00110 => 11001 => 10011 => 01011

00111 => 11000 => 10001 => 00101

01000 => 10111 => 01111 => 01111

01001 => 10110 => 01101 => 11001

01010 => 10101 => 01011 => 10011

01011 => 10100 => 01001 => 01001

01100 => 10011 => 00111 => 00111

01101 => 10010 => 00101 => 10001

01110 => 10001 => 00011 => 00011

01111 => 10000 => 00001 => 00001

10000 => 01111 => 11110 => 11110

10001 => 01110 => 11100 => 11010

10010 => 01101 => 11010 => 10110

10011 => 01100 => 11000 => 01010

10100 => 01011 => 10110 => 01110

10101 => 01010 => 10100 => 10010

10110 => 01001 => 10010 => 00110

10111 => 01000 => 10000 => 00010

11000 => 00111 => 01110 => 11100

11001 => 00110 => 01100 => 10100

11010 => 00101 => 01010 => 01100

11011 => 00100 => 01000 => 00100

11100 => 00011 => 00110 => 11000

11101 => 00010 => 00100 => 01000

11110 => 00001 => 00010 => 10000

11111 => 00000 => 00000 => 00000

000000 => 111111 => 111111 => 111111

000001 => 111110 => 111101 => 111101

000010 => 111101 => 111011 => 111011

000011 => 111100 => 111001 => 110101

000100 => 111011 => 110111 => 110111

000101 => 111010 => 110101 => 101101

000110 => 111001 => 110011 => 101011

000111 => 111000 => 110001 => 010101

001000 => 110111 => 101111 => 101111

001001 => 110110 => 101101 => 011101

001010 => 110101 => 101011 => 011011

001011 => 110100 => 101001 => 100101

001100 => 110011 => 100111 => 010111

001101 => 110010 => 100101 => 001101

001110 => 110001 => 100011 => 001011

001111 => 110000 => 100001 => 000101

010000 => 101111 => 011111 => 011111

010001 => 101110 => 011101 => 111001

010010 => 101101 => 011011 => 110011

010011 => 101100 => 011001 => 101001

010100 => 101011 => 010111 => 100111

010101 => 101010 => 010101 => 011001

010110 => 101001 => 010011 => 010011

010111 => 101000 => 010001 => 001001

011000 => 100111 => 001111 => 001111

011001 => 100110 => 001101 => 110001

011010 => 100101 => 001011 => 100011

011011 => 100100 => 001001 => 010001

011100 => 100011 => 000111 => 000111

011101 => 100010 => 000101 => 100001

011110 => 100001 => 000011 => 000011

011111 => 100000 => 000001 => 000001

100000 => 011111 => 111110 => 111110

100001 => 011110 => 111100 => 111010

100010 => 011101 => 111010 => 110110

100011 => 011100 => 111000 => 101010

100100 => 011011 => 110110 => 101110

100101 => 011010 => 110100 => 011010

100110 => 011001 => 110010 => 010110

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Map

complement

Description

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

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.