I was having difficulty with problem 46a in Stanley's Enumerative Combinatorics chapter 3 (page 111):
Let $f(n)$ be the number of sublattices of rank $n$ of the Boolean Algebra $B_n$. Show that $f(n)$ is also the number of partial orders $P$ on $[n]$.
I am not exactly sure what a sublattice of rank $n$ would look like, particularly in this case. I also don't know what a partial order on $[n]$ would look like either.
I would appreciate any help.