This is the nicest solution I've seen so far. I believe that for the operation of randomly sampling a single row, only the consecutiveness invariant is needed

This is the nicest solution I've seen so far. I believe that for the operation of randomly sampling a single row, only the consecutiveness invariant is needed. The random permutation invariant is unnecessary, because the choice from the range (1, N+1) is random anyway. However, I can imagine the random permutation invariant being useful for other operations (although I can't immediately think of one). EDIT: the random permutation invariant could maybe be useful for a list that can be displayed to the user. I can imagine some cases where it is nice to have an order that doesn't change a lot while you don't want it to depend on any property in particular (like the order in which the rows were added).