Enumerating Combinations (task 129)

This one has me stumped.

Here's the relevant function that I use to produce the string at a given index in the list of all permutations:

def index_to_lexstring(symbols, length, index):
    from math import factorial as fact
    from math import floor
    """
    Finds the string at <index> from a list of the lexicographically sorted
    permutations of <symbols> set of length <length>.
    INPUT: <index>, an integer; <symbols>, an iterable containing all symbols used.
    OUTPUT: the nth lexicographic ordered string
    """
    output = []
    symbols = [str(item) for item in symbols]
    n = 0
    p = len(symbols)
    q = length
    i = index

    #Calculate each symbol for the output list iteratively
    while (n < q):
        #Calculate the size of the complete permutations list.
        #Save as the denominator
        denominator = nCr(p-n-1, q-n-1) * fact(q-n-1)

        #Select the next symbol, add to output, remove from symbols
        output.append( symbols.pop( floor(i / denominator) ) )

        #Update iterative values
        i -= (denominator * floor(i / denominator))
        n += 1

    #Return a joined string of symbols in outlist
    return("".join(output))

On the first two test cases (5 3 2 and 30 15 0), it works fine. But on the third sample test case (36 16 7307872109), it fails, producing the output 012345679QBFPZYX instead of KLMNOPQRSTUVWXYZ.

Any ideas why?

Okay, I think I'm onto something. My output to your sample set is 012 021 102 120 201. But as you've noted, I seem to be calculating partial permutations instead of partial combinations.

I just spent a week skiing with friends, no programming. So I think I'm ready to reattack this problem now! Wish me luck.

Got it, finally!

For future reference of those following this... I was previously solving the factoradic problem. I needed to solve the combinadic problem. But half the fun was digging deep to find ideas, so I won't spoil it too much. ;)