[formal-methods] Conceptual Mathematics, I.1.6

[Josh Myer]

Conceptual Mathematics: Article I, Session 1, Exercise 6:

  How many maps f : A -> A satisfy (f o f) = f?

The answer is, as a first approximation, a metric fucktonne.  I'm
having a hard time pinning down a better approximation.  Does anyone
have a closed form in terms of |A| for this?  I'd be happy to talk it
through in email, but don't want to spoil other people's answering
processes.  (However, I feel no compunction about bursting folks' "1:
identity!" bubble.)

I need to bust out my combinatorics text and maybe TAoCP to look for
the right kind of generating function; I think that's where the answer
to this lies.  Generating functions always were a little magic...
-- 
Josh Myer   650.248.3796
  josh at joshisanerd.com