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Identifier
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
Images
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1011010101010100=>1101101010101001 1011100101010100=>1101101010101001 1011101001010100=>1101110010101001 1011110001010100=>1101110010101001 1011110111000000=>1101111011000001 1011111010100000=>1101111101000001 1011111011000000=>1101111101000001 1011111100010000=>1101111100100001 1011111100100000=>1101111101000001 1011111101000000=>1101111110000001 1011111110000000=>1101111110000001 1101010101010100=>1110101010101001 1110010101010100=>1110101010101001 1110100101010100=>1111001010101001 1111000101010100=>1111001010101001 1111011100000010=>1111101100000101 1111101010000010=>1111110100000101 1111101100000010=>1111110100000101 1111110001000010=>1111110010000101 1111110010000010=>1111110100000101 1111110100000010=>1111111000000101 1111111000000010=>1111111000000101 101010101010101010=>110101010101010101 101010101010101100=>110101010101010101 101010101010110100=>110101010101011001 101010101011010100=>110101010101101001 101010101101010100=>110101010110101001 101010110101010100=>110101011010101001 101011010101010100=>110101101010101001 101101010101010100=>110110101010101001 110101010101010100=>111010101010101001 101010101010111000=>110101010101011001 101010101011100100=>110101010101101001 101010101110010100=>110101010110101001 101010111001010100=>110101011010101001 101011100101010100=>110101101010101001 101110010101010100=>110110101010101001 111001010101010100=>111010101010101001 111111110000000010=>111111110000000101 101111111100000000=>110111111100000001 111111101000000010=>111111110000000101 101111111010000000=>110111111100000001 111111100100000010=>111111101000000101 111111011000000010=>111111101000000101 101111111001000000=>110111111010000001 101111110110000000=>110111111010000001 10101010101010101010=>11010101010101010101 10101010101010101100=>11010101010101010101 10101010101010110100=>11010101010101011001 10101010101011010100=>11010101010101101001 10101010101101010100=>11010101010110101001 10101010110101010100=>11010101011010101001 10101011010101010100=>11010101101010101001 10101101010101010100=>11010110101010101001 10110101010101010100=>11011010101010101001 11010101010101010100=>11101010101010101001 11111111100000000010=>11111111100000000101 10111111111000000000=>11011111111000000001 11111111010000000010=>11111111100000000101 10111111110100000000=>11011111111000000001 1111111111000000000010=>1111111111000000000101 1011111111110000000000=>1101111111110000000001
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Return the binary word with every valley replaced by a peak.
A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. This map replaces every valley with a peak.
References
[1] Tasoulas, I., Manes, K., Sapounakis, A., Tsikouras, P. Chains with small intervals in the lattice of binary paths MathSciNet:4054761
Properties
graded
Sage code
def mapping(w):
    w = list(w)
    f = list(w)
    for i in range(len(w)-1):
        if w[i:i+2] == [0, 1]:
            f[i:i+2] = [1, 0]
    if w[len(w)-1] == 0:
        f[len(w)-1] = 1
    return Words([0,1])(f)
Weight
40
Created
May 19, 2021 at 17:35 by Martin Rubey
Updated
May 19, 2021 at 17:35 by Martin Rubey