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Math Help - monotonicity

  1. #1
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    UKRAIN
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    4

    monotonicity

    Hi ever body,
    could you please let me know how I can prove the following problem.

    for some $A,B \subseteq [n]$ such that for any $x\in\{0,1\}$ we have two function s.t. $r(x)=(-1)^{\varSigma_{i \in A}x_i}$ and $t(x)=(-1)^{\varSigma_{i \in B}x_i}$ and suppose that $f(x)$ is function depends on r and
    t
     f^\prime(x) = \left \{\begin{array}{l}+\infty \hspace*{0.8cm} if  \hspace*{0.3cm} wt(x) \geq n/2 + 4\delta \\ f(x) \hspace*{0.8cm} if  \hspace*{0.3cm} n/2 - 4\delta \leq wt(x) \leq n/2 + 4\delta \\-\infty  \hspace*{0.8cm} if \hspace*{0.3cm} wt(x) \leq n/2 - 4\delta \end{array}  \right . \begin{array}{l} \end{array}

    wt(x) is the bitstrings hamming weight of size n \in \{0,1\}^n

    How we could prove that if $A \cap B = \emptyset $ then $f^{\prime}$ is monotone.

    Cheers,
    Last edited by ghali; September 19th 2012 at 11:21 AM.
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