Indexing subsets of size k
I think you could do this by recursively narrowing down ranges, right? You know that all subsets beginning with a given integer will be adjacent, and that for a given first element d there will be (n - d) choose (k-1) of them. You can skip ahead as far as necessary in the virtual list of subsets until you're in the range of subsets beginning with the first element of the target sorted subset, then recurse to narrow it down precisely.
EG, suppose n=20, k=6. If your target subset is {5, 8, 12, 14, 19}, none of the subsets beginning with 1-4 are valid choices. You know that the index first subset beginning with 5 will be ((19 choose 5) + (18 choose 5) + (17 choose 5) + (16 choose 5)). Call that index i0. Now you have (15 choose 5) subsets that all begin with 5 to index into, and none of the ones beginning with 5, 1-7... are interesting. (14 choose 4) of them start with 1, (13 choose 4) start with 2, etc. So the index of the first set beginning with 5, 8 will be i0 + (14 choose 4) + (13 choose 4) + (12 choose 4) + (11 choose 4) + (10 choose 4) + (9 choose 4) + (8 choose 4). Etc.
Writing the algorithm out is kind of painful, but I think it should work nicely with a computer keeping track of the fiddly details.
There are n choose k subsets of {1,2,...,n} of size k. These can be naturally ordered by sorting the elements and using the lexigraphical order. 
Is there a fast way to determine the index of a given subset, i.e. its index in the sorted list of all subsets of size k? One method would be to create a dictionary from subsets to indices by enumerating all subsets of size k, but this requires n choose k space and time. For my application n and k are infeasibly large, but I only need to determine the indices of comparatively few subsets.
I'm coding in Python, but I'm more interested in a general algorithm than any specific implementation. Of course, if there's an especially fast way to do this in Python that would be great.
Motivation: The subsets of {1,2,...,n} of size k correspond bijectively to basis vectors of the kth exterior power of a vector space with dimension n. I'm performing computations in the exterior algebra of a vector space and trying to convert the resulting lists of vectors into sparse matrices to do linear algebra, and to do that I need to index the vectors by integers rather than by lists.