Please forgive me if my terminology is lacking. I have been thinking about permutations and it occurs to me that some permutations are very easy to describe, while other are much more difficult. For a set $\{0,1,...,N-1\}$ there are $N!$ possible permutations. You could describe a particular permutation with something like a lookup table, or you could describe it using a bijective function. Take the identity permutation for example. It can be described simply with $f(x)=x$ which is much simpler then listing an entire $N$ element table. But for some permutations I imagine that the function necessary to describe it would be just as complicated as listing the entire table.
I'd be interested to know how many of the $N!$ permutations fall into this category of being much simpler to describe by formula than by table, and how many fall into the category of being so complicated that table notation is just as efficient as a formula. Where can I look for information on this?
