Generation of Derangements
One of the current threads for the evolution of Algorithm::Combinatorics is researching the generation of derangements (i.e., permutations with no fixed points).
Looks like derangements are hard to generate efficiently. The most promising reference I've found by now is this paper from 2004 by James F. Korsh, and Paul S. LaFollette, Constant time generation of derangements.
Unfortunately I have not been able to find a copy online, so I wrote to the authors today asking whether it can be obtained somehow.