# Finding upper bound on number of I/Os needed to generate all permutations of some input in external memory

The general approach outlined in this paper in its proof of the lower bound on the average number of I/Os needed to obtain a given permutation of some input in external memory is as follows. Note that $$N$$ is the number of items to be permuted and $$t$$ has no prior definition in the paper.

Why are they trying to find the value of $$t$$ for which the bound on the number of possible permutations generated after $$t$$ I/Os is only $$\frac{N!}{2}$$ instead of $$N!$$? I realize that $$\frac{N!}{2}$$ gives the number of orderings of $$n$$ elements, but just because you can obtain one permutation after $$t$$ I/Os does not necessarily mean that you can obtain its reverse permutation after $$t$$ I/Os.