I What does the product part of Laughlin wave function mean?

[George Keeling]

TL;DR Summary

confused by product symbol with two subscripts

I am looking at the Laughlin wave function and it contains the term
$$\prod_{j<k}^{N}\left(z_j-z_k\right)^q$$
In Wikipedia the lower index on $\Pi$ is $1\le i<j\le N$ and there is no upper index. I'm not sure what either mean. For example would
$$\prod_{j<k}^{N}\left(z_j-z_k\right)^q=\prod_{k=2}^{N}\left[\prod_{j=1}^{k-1}\left(z_j-z_k\right)^q\right]?$$
(It seems that $k$ cannot be 1 because there would be nothing to multiply in the second product). I'm not sure what else the expression could mean.

For $N=3$ that would give $\ \left(z_1-z_2\right)^q\left(z_1-z_3\right)^q\left(z_2-z_3\right)^q$ I think.

 

[gentzen]

Yes, this is the meaning of that product symbol with two subscripts.