What does it mean when a Sigma has two variables at the bottom
By Emma Martinez •
In a paper I'm reading there is a sigma notation that I'm not understanding. They have two variables at the bottom of the sigma.
From the paper:
A finite set of requirements Req = {r1,...,rn} and D is a distribution, satisfying the following normalization property: $$ \sum\limits_{r_i,r_j} D(r_i,r_j) = 1 $$
So does that mean that we are going to sum all of the combinations of ri and rj where i != j? So if n=5 we would have (5 choose 2) = 10 combinations to sum. Is that right?
Thank you.
$\endgroup$ 01 Answer
$\begingroup$You have $$\sum\limits_{r_i,r_j} D(r_i,r_j) = \sum_{i=1}^n \sum_{j=1}^n D(r_i,r_j)$$
Which means that the sum is over all combinations $(i,j) \in \{1, \dots ,n\}^2$. Not only the ones for which $i \neq j$. The notation for this last case would be $$\sum_{i \neq j} D(r_i,r_j).$$
$\endgroup$ 2
