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Identifier
Mp00158: Binary words alternating inverseBinary words
Images
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110100111101001001101000=>100001101000011100111101 110100111011011010000100=>100001101110001111010001 110100111011101001000100=>100001101110111100010001 110100111101001101000100=>100001101000011000010001 110100111101101000100100=>100001101000111101110001 110100111110100100100100=>100001101011110001110001 110110100011011011010000=>100011110110001110000101 110110100011011101001000=>100011110110001000011101 110110100011101001101000=>100011110110111100111101 110110100011101101000100=>100011110110111000010001 110110100011110100100100=>100011110110100001110001 111010010011011011010000=>101111000110001110000101 111010010011011101001000=>101111000110001000011101 111010010011101001101000=>101111000110111100111101 111010010011101101000100=>101111000110111000010001 111010010011110100100100=>101111000110100001110001 110110110100001101101000=>100011100001011000111101 110110110100001110100100=>100011100001011011110001 110111010010001101101000=>100010000111011000111101 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111010011101101000100010=>101111001000111101110111 111010011110100100100010=>101111001011110001110111 111011010001101101000010=>101110000100111000010111 111011010001110100100010=>101110000100100001110111 111101001001101101000010=>101000011100111000010111 111101001001110100100010=>101000011100100001110111 111011011010000110100010=>101110001111010011110111 111011101001000110100010=>101110111100010011110111 111101001101000110100010=>101000011000010011110111 111101101000100110100010=>101000111101110011110111 111110100100100110100010=>101011110001110011110111 111011011011010000010010=>101110001110000101000111 111011011101001000010010=>101110001000011101000111 111011101001101000010010=>101110111100111101000111 111011101101000100010010=>101110111000010001000111 111011110100100100010010=>101110100001110001000111 111101001101101000010010=>101000011000111101000111 111101001110100100010010=>101000011011110001000111 111101101000110100010010=>101000111101100001000111 111110100100110100010010=>101011110001100001000111 111101101101000010010010=>101000111000010111000111 111101110100100010010010=>101000100001110111000111 111110100110100010010010=>101011110011110111000111 111110110100010010010010=>101011100001000111000111 111111010010010010010010=>101010000111000111000111 111111111110000000000100=>101010101011010101010001 110111111111100000000000=>100010101010110101010101 11111111111111111111111100000=>10101010101010101010101001010
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
21
Created
Sep 04, 2020 at 16:31 by Christian Stump
Updated
Sep 04, 2020 at 16:31 by Christian Stump