- FindStat

Identifier

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

Images

0 => 0 => 0 => 0

1 => 1 => 1 => 1

00 => 00 => 00 => 00

01 => 10 => 10 => 01

10 => 01 => 01 => 10

11 => 11 => 11 => 11

000 => 000 => 000 => 000

001 => 010 => 100 => 001

010 => 100 => 010 => 010

011 => 110 => 110 => 011

100 => 001 => 001 => 100

101 => 011 => 011 => 110

110 => 101 => 101 => 101

111 => 111 => 111 => 111

0000 => 0000 => 0000 => 0000

0001 => 0010 => 1000 => 0001

0010 => 0100 => 0100 => 0010

0011 => 0110 => 1100 => 0011

0100 => 1000 => 0010 => 0100

0101 => 1010 => 0110 => 0110

0110 => 1100 => 1010 => 0101

0111 => 1110 => 1110 => 0111

1000 => 0001 => 0001 => 1000

1001 => 0011 => 0011 => 1100

1010 => 0101 => 1001 => 1001

1011 => 0111 => 0111 => 1110

1100 => 1001 => 0101 => 1010

1101 => 1011 => 1011 => 1101

1110 => 1101 => 1101 => 1011

1111 => 1111 => 1111 => 1111

00000 => 00000 => 00000 => 00000

00001 => 00010 => 10000 => 00001

00010 => 00100 => 01000 => 00010

00011 => 00110 => 11000 => 00011

00100 => 01000 => 00100 => 00100

00101 => 01010 => 01100 => 00110

00110 => 01100 => 10100 => 00101

00111 => 01110 => 11100 => 00111

01000 => 10000 => 00010 => 01000

01001 => 10010 => 00110 => 01100

01010 => 10100 => 10010 => 01001

01011 => 10110 => 01110 => 01110

01100 => 11000 => 01010 => 01010

01101 => 11010 => 10110 => 01101

01110 => 11100 => 11010 => 01011

01111 => 11110 => 11110 => 01111

10000 => 00001 => 00001 => 10000

10001 => 00011 => 00011 => 11000

10010 => 00101 => 10001 => 10001

10011 => 00111 => 00111 => 11100

10100 => 01001 => 01001 => 10010

10101 => 01011 => 10011 => 11001

10110 => 01101 => 11001 => 10011

10111 => 01111 => 01111 => 11110

11000 => 10001 => 00101 => 10100

11001 => 10011 => 01011 => 11010

11010 => 10101 => 01101 => 10110

11011 => 10111 => 10111 => 11101

11100 => 11001 => 10101 => 10101

11101 => 11011 => 11011 => 11011

11110 => 11101 => 11101 => 10111

11111 => 11111 => 11111 => 11111

000000 => 000000 => 000000 => 000000

000001 => 000010 => 100000 => 000001

000010 => 000100 => 010000 => 000010

000011 => 000110 => 110000 => 000011

000100 => 001000 => 001000 => 000100

000101 => 001010 => 011000 => 000110

000110 => 001100 => 101000 => 000101

000111 => 001110 => 111000 => 000111

001000 => 010000 => 000100 => 001000

001001 => 010010 => 001100 => 001100

001010 => 010100 => 100100 => 001001

001011 => 010110 => 011100 => 001110

001100 => 011000 => 010100 => 001010

001101 => 011010 => 101100 => 001101

001110 => 011100 => 110100 => 001011

001111 => 011110 => 111100 => 001111

010000 => 100000 => 000010 => 010000

010001 => 100010 => 000110 => 011000

010010 => 100100 => 100010 => 010001

010011 => 100110 => 001110 => 011100

010100 => 101000 => 010010 => 010010

010101 => 101010 => 100110 => 011001

010110 => 101100 => 110010 => 010011

010111 => 101110 => 011110 => 011110

011000 => 110000 => 001010 => 010100

011001 => 110010 => 010110 => 011010

011010 => 110100 => 011010 => 010110

011011 => 110110 => 101110 => 011101

011100 => 111000 => 101010 => 010101

011101 => 111010 => 110110 => 011011

011110 => 111100 => 111010 => 010111

011111 => 111110 => 111110 => 011111

100000 => 000001 => 000001 => 100000

100001 => 000011 => 000011 => 110000

100010 => 000101 => 100001 => 100001

100011 => 000111 => 000111 => 111000

100100 => 001001 => 010001 => 100010

100101 => 001011 => 100011 => 110001

100110 => 001101 => 110001 => 100011

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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

reverse

Description

Return the reversal of a binary word.