- FindStat

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Identifier

Mp00200: Binary words —twist⟶ Binary words

Images

0 => 1

1 => 0

00 => 10

01 => 11

10 => 00

11 => 01

000 => 100

001 => 101

010 => 110

011 => 111

100 => 000

101 => 001

110 => 010

111 => 011

0000 => 1000

0001 => 1001

0010 => 1010

0011 => 1011

0100 => 1100

0101 => 1101

0110 => 1110

0111 => 1111

1000 => 0000

1001 => 0001

1010 => 0010

1011 => 0011

1100 => 0100

1101 => 0101

1110 => 0110

1111 => 0111

00000 => 10000

00001 => 10001

00010 => 10010

00011 => 10011

00100 => 10100

00101 => 10101

00110 => 10110

00111 => 10111

01000 => 11000

01001 => 11001

01010 => 11010

01011 => 11011

01100 => 11100

01101 => 11101

01110 => 11110

01111 => 11111

10000 => 00000

10001 => 00001

10010 => 00010

10011 => 00011

10100 => 00100

10101 => 00101

10110 => 00110

10111 => 00111

11000 => 01000

11001 => 01001

11010 => 01010

11011 => 01011

11100 => 01100

11101 => 01101

11110 => 01110

11111 => 01111

000000 => 100000

000001 => 100001

000010 => 100010

000011 => 100011

000100 => 100100

000101 => 100101

000110 => 100110

000111 => 100111

001000 => 101000

001001 => 101001

001010 => 101010

001011 => 101011

001100 => 101100

001101 => 101101

001110 => 101110

001111 => 101111

010000 => 110000

010001 => 110001

010010 => 110010

010011 => 110011

010100 => 110100

010101 => 110101

010110 => 110110

010111 => 110111

011000 => 111000

011001 => 111001

011010 => 111010

011011 => 111011

011100 => 111100

011101 => 111101

011110 => 111110

011111 => 111111

100000 => 000000

100001 => 000001

100010 => 000010

100011 => 000011

100100 => 000100

100101 => 000101

100110 => 000110

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click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

Return the binary word with first letter inverted.

Properties

bijective, graded, involutive

Sage code

def mapping(w):
    if w:
        return Words([0,1], len(w))([1-w[0]] + list(w[1:]))

Weight

Created

Dec 06, 2020 at 19:36 by Martin Rubey

Updated

Oct 14, 2024 at 22:53 by Nadia Lafreniere