Partially ordered set
Number of partial orders

Partially ordered set

Section Title: Number of partial orders
Table Section Text: None

Elem­ents	Any	Transitive	Reflexive	Preorder	Partial order	Total preorder	Total order	Equivalence relation

0	1	1	1	1	1	1	1	1

1	2	2	1	1	1	1	1	1

2	16	13	4	4	3	3	2	2

3	512	171	64	29	19	13	6	5

4	65,536	3,994	4,096	355	219	75	24	15

n	2n2	2n2−n	∑n k=0 k! S(n, k)	n!	∑n k=0 S(n, k)

OEIS	A002416	A006905	A053763	A000798	A001035	A000670	A000142	A000110

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