Enumeration
The number of abstract simplicial complexes on n elements is the nth Dedekind number. These numbers grow very rapidly, and are known only for n ≤ 8; they are
- 2, 3, 6, 20, 168, 7581, 7828354, 2414682040998, 56130437228687557907788 (sequence A000372 in OEIS).
Read more about this topic: Abstract Simplicial Complex