Dedekind Numbers
The number of different Sperner families on a set of n elements is counted by the Dedekind numbers, the first few of which are
- 2, 3, 6, 20, 168, 7581, 7828354, 2414682040998, 56130437228687557907788 (sequence A000372 in OEIS).
Although accurate asymptotic estimates are known for larger values of n, it is unknown whether there exists an exact formula that can be used to compute these numbers efficiently.
Read more about this topic: Sperner Family
Famous quotes containing the word numbers:
“The forward Youth that would appear
Must now forsake his Muses dear,
Nor in the Shadows sing
His Numbers languishing.”
—Andrew Marvell (1621–1678)