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Identifier

Mp00135: Binary words —rotate front-to-back⟶ Binary words

Images

0 => 0

1 => 1

00 => 00

01 => 10

10 => 01

11 => 11

000 => 000

001 => 010

010 => 100

011 => 110

100 => 001

101 => 011

110 => 101

111 => 111

0000 => 0000

0001 => 0010

0010 => 0100

0011 => 0110

0100 => 1000

0101 => 1010

0110 => 1100

0111 => 1110

1000 => 0001

1001 => 0011

1010 => 0101

1011 => 0111

1100 => 1001

1101 => 1011

1110 => 1101

1111 => 1111

00000 => 00000

00001 => 00010

00010 => 00100

00011 => 00110

00100 => 01000

00101 => 01010

00110 => 01100

00111 => 01110

01000 => 10000

01001 => 10010

01010 => 10100

01011 => 10110

01100 => 11000

01101 => 11010

01110 => 11100

01111 => 11110

10000 => 00001

10001 => 00011

10010 => 00101

10011 => 00111

10100 => 01001

10101 => 01011

10110 => 01101

10111 => 01111

11000 => 10001

11001 => 10011

11010 => 10101

11011 => 10111

11100 => 11001

11101 => 11011

11110 => 11101

11111 => 11111

000000 => 000000

000001 => 000010

000010 => 000100

000011 => 000110

000100 => 001000

000101 => 001010

000110 => 001100

000111 => 001110

001000 => 010000

001001 => 010010

001010 => 010100

001011 => 010110

001100 => 011000

001101 => 011010

001110 => 011100

001111 => 011110

010000 => 100000

010001 => 100010

010010 => 100100

010011 => 100110

010100 => 101000

010101 => 101010

010110 => 101100

010111 => 101110

011000 => 110000

011001 => 110010

011010 => 110100

011011 => 110110

011100 => 111000

011101 => 111010

011110 => 111100

011111 => 111110

100000 => 000001

100001 => 000011

100010 => 000101

100011 => 000111

100100 => 001001

100101 => 001011

100110 => 001101

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Description

The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.

Properties

bijective, graded

Sage code

def mapping(w):
    return Word([int(l) for l in w[1:]] + [int(w[0])], [0,1])

Weight

Created

Jan 29, 2020 at 13:27 by FindStatCrew

Updated

Jan 29, 2020 at 13:27 by Martin Rubey