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Let $a=a_1,a_2,...,a_n$ and $b=b_1,b_2,...,b_n$ be two sequence of real numbers. Define

$$D(a,b) := \sum_{\{i,j\}}\sum_{\{k,l\}}{(|a_i-a_j||b_k-b_l|-|a_k-a_l||b_i-b_j|)^2} .$$

Does this parameter have a name? I just need some reference if there's any.

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  • $\begingroup$ Isn't this always zero? $\endgroup$
    – Wojowu
    Feb 10, 2017 at 16:31
  • $\begingroup$ Every term $|a_p-a_q||b_r-b_s|$ appears twice, once with a positive sign when $\{i,j\}=\{p,q\},\{k,l\}=\{r,s\}$, once with a negative sign when $\{i,j\}=\{r,s\},\{k,l\}=\{p,q\}$. $\endgroup$
    – Wojowu
    Feb 10, 2017 at 16:41
  • $\begingroup$ @Wojowu: Yes, you are right. Thanks. I have a typo. I edit my question. $\endgroup$
    – j.s.
    Feb 10, 2017 at 16:48
  • $\begingroup$ since it is a sum of squares it can only be zero if every summand is zero $\endgroup$
    – user35593
    Feb 10, 2017 at 22:28

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