Suppose is a collection of subsets of that is an antichain with regards to inclusion.
Show that
There is a very nice probabilistic proof of this. Note also that it is easy to deduce from this that
Moderator approved: MF
Suppose is a collection of subsets of that is an antichain with regards to inclusion.
Show that
There is a very nice probabilistic proof of this. Note also that it is easy to deduce from this that
Moderator approved: MF
I had a novel thought, but never carried through with it. Namely, there's an obvious -action on the set of all antichains of by sending to . I was moderately sure then that from where the conclusion immediately follows. Never worked it out though--maybe I will some other time (assuming it's right).
Nice proof though! I like it.