You too! I started thinking about the original question again - how to find duplets etc for Z_n. Algebraic approach is the same, but the homometric subsets which are not congruent in Z can very well be congruent in Z_n, so that needs to be taken care of rather carefully...

Over here, I'm trying to calculate the multiplets for n=29 k=8. An I'm wondering if it is possible to define a sorting technique that gives me a 'normalized' representative of all binary bracelets in polynomial form such that it is invariant under appending extra zero's. Think 'binary numbers' : they are invariant under prepending zero's.

I think this is not a good direction to go - after that, will you do k = 9 and so on? I mean that in my opinion this simply would not be a very interesting result, since you already have calculated so many of the multiplets. A more interesting (again, imho) would be to find the minimal multiplets - with the minimal possible k (and possibly n): doublets, triplets.

This looks like a challenge from the computational viewpoint. I am sure that minimal doublets could be found relatively quickly, but triplets etc - not so sure.