What does Rasch mean in the last sentence?

Here x has two subscripts, v and i, where v is taking on values from 1 to n, and i is taking on values from 1 to k.

Something like x_(1,.) would represent the sum of all of the x values where v=1:  x_(1,.) = x_(1,1) + x_(1,2) + x_(1,3) + ... + x_(1,k).

And, something like x_(.,1) would represent the sum of all the x values where i = 1:  x_(.,1) = x_(1,1) + x_(2,1) + x_(3,1) + ... + x_(n,1)

ETA: In my writing above, the numbers in the brackets are subscripts of x

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