Given a kelement subset, remove any of the k elements, this clearly is a permutation of k1 elements.
Take a set (k1)element subsets of the same k1 elements. There are k! remaining elements that can be placed back into the (k1)element subsets. Now, there are exactly k repeated kelement subsets doing this process, so there are only (k1)! that can be added to each set of permutations. Now there are (k1)! permutations, and (k1)! elements that can be added to those permutations, adding an element to each permutation out of the possible (k1)! elements gives a distinct kelement subset.
Therefore, bijection.

is that what you were looking for, or am I off?
Last fiddled with by jebeagles on 20060504 at 01:04
