- FindStat

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Identifier

Mp00158: Binary words —alternating inverse⟶ Binary words

Images

0 => 0

1 => 1

00 => 01

01 => 00

10 => 11

11 => 10

000 => 010

001 => 011

010 => 000

011 => 001

100 => 110

101 => 111

110 => 100

111 => 101

0000 => 0101

0001 => 0100

0010 => 0111

0011 => 0110

0100 => 0001

0101 => 0000

0110 => 0011

0111 => 0010

1000 => 1101

1001 => 1100

1010 => 1111

1011 => 1110

1100 => 1001

1101 => 1000

1110 => 1011

1111 => 1010

00000 => 01010

00001 => 01011

00010 => 01000

00011 => 01001

00100 => 01110

00101 => 01111

00110 => 01100

00111 => 01101

01000 => 00010

01001 => 00011

01010 => 00000

01011 => 00001

01100 => 00110

01101 => 00111

01110 => 00100

01111 => 00101

10000 => 11010

10001 => 11011

10010 => 11000

10011 => 11001

10100 => 11110

10101 => 11111

10110 => 11100

10111 => 11101

11000 => 10010

11001 => 10011

11010 => 10000

11011 => 10001

11100 => 10110

11101 => 10111

11110 => 10100

11111 => 10101

000000 => 010101

000001 => 010100

000010 => 010111

000011 => 010110

000100 => 010001

000101 => 010000

000110 => 010011

000111 => 010010

001000 => 011101

001001 => 011100

001010 => 011111

001011 => 011110

001100 => 011001

001101 => 011000

001110 => 011011

001111 => 011010

010000 => 000101

010001 => 000100

010010 => 000111

010011 => 000110

010100 => 000001

010101 => 000000

010110 => 000011

010111 => 000010

011000 => 001101

011001 => 001100

011010 => 001111

011011 => 001110

011100 => 001001

011101 => 001000

011110 => 001011

011111 => 001010

100000 => 110101

100001 => 110100

100010 => 110111

100011 => 110110

100100 => 110001

100101 => 110000

>>> Load all 8514 entries. <<<

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

Description

Sends a binary word

$w_1\cdots w_m$ to the binary word

$v_1 \cdots v_m$ with

$v_i = w_i$ if

$i$ is odd and

$v_i = 1 - w_i$ if

$i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.

References

[1] Karp, S. N., Williams, L. K. The m=1 amplituhedron and cyclic hyperplane arrangements arXiv:1608.08288

Properties

bijective, graded, involutive

Sage code

def mapping(w):
    P = w.parent()
    v = list(w)
    for i in range(len(v)):
        if is_odd(i):
            v[i] = 1-v[i]
    return P(v)

Weight

Created

Sep 04, 2020 at 16:31 by Christian Stump

Updated

Sep 04, 2020 at 16:31 by Christian Stump