## How many inclusion preserving maps of subsets?

Let S be a set with n elements and Σk={R⊆S∣|R|=k}. For k≤n/2 how many bijections f are there between Σk and Σn−k, such that x⊆f(x)? For k=1 clearly the answer is the number of derangements of order n. I’m really mostly curious about the case n=2k+1, and even then I would just be happy with … Read more