What's the difference between derangements and partial derangements?

Question

What's the difference between derangements and partial derangements?

I know that derangements are essentially subfactorials; could anyone explain the difference? I came across this in some local recreational math book...

Answer 1

A quick read through their definitions here should answer it...

Derangement a.k.a subfactorial : http://en.wikipedia.org/wiki/Derangement

Rencontres numbers a.k.a partial derangements : http://en.wikipedia.org/wiki/Rencontres_numbers

Answer 2

I'm answering this question myself as a reference answer from the wiki for the partial derangements. (from @kugel ).

Essentially, The Rencontres Numbers are a triangular array of integers that enumerate permutations of the set { 1, ..., n } with specified numbers of fixed points: in other words, partial derangements, while derangements are permutations of the elements of a set, such that no element appears in their original position.