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Identifier
Mp00278: Binary words rowmotionBinary words
Images
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110011000101=>011100011010 110011001001=>011100110010 110011010001=>011101100010 110011100001=>011100001110 110100010101=>111000101010 110100011001=>111000100110 110100100101=>111001001010 110100101001=>111001010010 110100110001=>111001000110 110101000101=>111010001010 110101001001=>111010010010 110101010001=>111010100010 110101100001=>111010000110 110110000101=>111000011010 110110001001=>111000110010 110110010001=>111001100010 110110100001=>111011000010 110111000001=>111000001110 111000010101=>000111101010 111000101001=>001111010010 111001000101=>011110001010 111001001001=>011110010010 111001010001=>011110100010 111010001001=>111100010010 111010100001=>111101000010 111100000101=>000011111010 111100001001=>000111110010 111100010001=>001111100010 111100100001=>011111000010 111101000001=>111110000010 10101010101010=>11010101010100 10101010101100=>11010101010001 10101010110100=>11010101011000 10101010111000=>11010101000011 10101011010100=>11010101101000 10101011100100=>11010100111000 10101011101000=>11010101110000 10101011110000=>11010100000111 10101101010100=>11010110101000 10101110010100=>11010011101000 10101110100100=>11010111001000 10101110101000=>11010111010000 10101110110000=>11010111000001 10101111000100=>11010001111000 10101111010000=>11010111100000 10110101010100=>11011010101000 10110111100000=>11011000000111 10111001010100=>11001110101000 10111010010100=>11011100101000 10111010100100=>11011101001000 10111011000100=>11011100011000 10111011010000=>11011101100000 10111011100000=>11011100000011 10111100010100=>11000111101000 10111100110000=>11001111000001 10111101000100=>11011110001000 10111101001000=>11011110010000 10111101010000=>11011110100000 10111101100000=>11011110000001 10111110000100=>11000011111000 10111110001000=>11000111110000 10111110010000=>11001111100000 10111110100000=>11011111000000 10111111000000=>11000000011111 11001111100000=>01110000001111 11010101010100=>11101010101000 11010101011000=>11101010100001 11010101100100=>11101010011000 11010101101000=>11101010110000 11010101110000=>11101010000011 11010110010100=>11101001101000 11010110011000=>11101001100001 11010110100100=>11101011001000 11010110101000=>11101011010000 11010110110000=>11101011000001 11010111000100=>11101000111000 11010111001000=>11101001110000 11010111010000=>11101011100000 11010111100000=>11101000000111 11011001010100=>11100110101000 11011001011000=>11100110100001 11011001100100=>11100110011000 11011001101000=>11100110110000 11011001110000=>11100110000011 11011010010100=>11101100101000 11011010011000=>11101100100001 11011010100100=>11101101001000 11011010101000=>11101101010000 11011010110000=>11101101000001 11011011000100=>11101100011000 11011011001000=>11101100110000 11011011010000=>11101101100000 11011011100000=>11101100000011 11011100010100=>11100011101000 11011100011000=>11100011100001 11011100100100=>11100111001000 11011100101000=>11100111010000 11011100110000=>11100111000001 11011101000100=>11101110001000 11011101001000=>11101110010000 11011101010000=>11101110100000 11011101100000=>11101110000001 11011110000010=>11100000111100 11011110000100=>11100001111000 11011110001000=>11100011110000 11011110010000=>11100111100000 11011110100000=>11101111000000 11011111000000=>11100000001111 11100101010100=>01111010101000 11100101011000=>01111010100001 11100101100100=>01111010011000 11100101101000=>01111010110000 11100101110000=>01111010000011 11100110010100=>01111001101000 11100110011000=>01111001100001 11100110100100=>01111011001000 11100110101000=>01111011010000 11100110110000=>01111011000001 11100111000100=>01111000111000 11100111001000=>01111001110000 11100111010000=>01111011100000 11100111100000=>01111000000111 11101001010100=>11110010101000 11101001011000=>11110010100001 11101001100100=>11110010011000 11101001101000=>11110010110000 11101001110000=>11110010000011 11101010010100=>11110100101000 11101010011000=>11110100100001 11101010100100=>11110101001000 11101010101000=>11110101010000 11101010110000=>11110101000001 11101011000100=>11110100011000 11101011001000=>11110100110000 11101011010000=>11110101100000 11101011100000=>11110100000011 11101100010100=>11110001101000 11101100011000=>11110001100001 11101100100100=>11110011001000 11101100101000=>11110011010000 11101100110000=>11110011000001 11101101000010=>11110110000100 11101101000100=>11110110001000 11101101001000=>11110110010000 11101101010000=>11110110100000 11101101100000=>11110110000001 11101110000010=>11110000011100 11101110000100=>11110000111000 11101110001000=>11110001110000 11101110010000=>11110011100000 11101110100000=>11110111000000 11101111000000=>11110000000111 11110001010100=>00111110101000 11110001011000=>00111110100001 11110001100100=>00111110011000 11110001101000=>00111110110000 11110001110000=>00111110000011 11110010010100=>01111100101000 11110010011000=>01111100100001 11110010100100=>01111101001000 11110010101000=>01111101010000 11110010110000=>01111101000001 11110011000010=>01111100001100 11110011000100=>01111100011000 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1011010101010100=>1101101010101000 1011100101010100=>1100111010101000 1011101001010100=>1101110010101000 1011110001010100=>1100011110101000 1011110111000000=>1101111000000011 1011111010100000=>1101111101000000 1011111011000000=>1101111100000001 1011111100010000=>1100011111100000 1011111100100000=>1100111111000000 1011111101000000=>1101111110000000 1011111110000000=>1100000000111111 1101010101010100=>1110101010101000 1110010101010100=>0111101010101000 1110100101010100=>1111001010101000 1111000101010100=>0011111010101000 1111011100000010=>1111100000011100 1111101010000010=>1111110100000100 1111101100000010=>1111110000001100 1111110001000010=>0011111110000100 1111110010000010=>0111111100000100 1111110100000010=>1111111000000100 1111111000000010=>0000001111111100 101010101010101010=>110101010101010100 101010101010101100=>110101010101010001 101010101010110100=>110101010101011000 101010101011010100=>110101010101101000 101010101101010100=>110101010110101000 101010110101010100=>110101011010101000 101011010101010100=>110101101010101000 101101010101010100=>110110101010101000 110101010101010100=>111010101010101000 101010101010111000=>110101010101000011 101010101011100100=>110101010100111000 101010101110010100=>110101010011101000 101010111001010100=>110101001110101000 101011100101010100=>110100111010101000 101110010101010100=>110011101010101000 111001010101010100=>011110101010101000 111111110000000010=>000000011111111100 101111111100000000=>110000000001111111 111111101000000010=>111111110000000100 101111111010000000=>110111111100000000 111111100100000010=>011111111000000100 111111011000000010=>111111100000001100 101111111001000000=>110011111110000000 101111110110000000=>110111111000000001 10101010101010101010=>11010101010101010100 10101010101010101100=>11010101010101010001 10101010101010110100=>11010101010101011000 10101010101011010100=>11010101010101101000 10101010101101010100=>11010101010110101000 10101010110101010100=>11010101011010101000 10101011010101010100=>11010101101010101000 10101101010101010100=>11010110101010101000 10110101010101010100=>11011010101010101000 11010101010101010100=>11101010101010101000 11111111100000000010=>00000000111111111100 10111111111000000000=>11000000000011111111 11111111010000000010=>11111111100000000100 10111111110100000000=>11011111111000000000 1111111111000000000010=>0000000001111111111100 1011111111110000000000=>1100000000000111111111
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Return the rowmotion of the binary word, regarded as an order ideal in the product of two chains.
In particular, this operation preserves the number of ones, and its order is the length of the word, see section 3.3 of [1].
References
[1] , Propp, J., Roby, T. Homomesy in products of two chains MathSciNet:3367853 arXiv:1310.5201
Properties
bijective, graded
Sage code
def mapping(w):
    if len(w) <= 1:
        return w
    r_w = []
    factor = []
    i = 0
    while i < len(w):
        if i + 1 < len(w) and (not w[i] and w[i+1]):
            r_w.extend(reversed(factor))
            factor = []
            r_w.extend([1, 0])
            i += 2
        else:
            factor.append(w[i])
            i += 1
    r_w.extend(reversed(factor))
    return Word(r_w)

Weight
40
Created
Jan 07, 2023 at 17:42 by Martin Rubey
Updated
Jan 07, 2023 at 17:42 by Martin Rubey