The Boolean lattice 
is the partially ordered set consisting of
all subsets of an 
-set, ordered by inclusion.
Equivalently, it is the power set of an 
-set regarded as a lattice with
meet and join given by intersection
and union, respectively.
The elements of rank 
in 
are the 
-element
subsets, so the 
th
rank has 
elements. The Hasse diagram of 
is the 
-hypercube graph.
