Reflexive Relation - Number of Reflexive Relations

Number of Reflexive Relations

The number of reflexive relations on an n-element set is 2n2−n.

Number of n-element binary relations of different types
n all 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 65536 3994 4096 355 219 75 24 15
OEIS A002416 A006905 A053763 A000798 A001035 A000670 A000142 A000110

Read more about this topic:  Reflexive Relation

Famous quotes containing the words number of, number and/or relations:

    He is the greatest artist who has embodied, in the sum of his works, the greatest number of the greatest ideas.
    John Ruskin (1819–1900)

    As equality increases, so does the number of people struggling for predominance.
    Mason Cooley (b. 1927)

    When any one of our relations was found to be a person of a very bad character, a troublesome guest, or one we desired to get rid of, upon his leaving my house I ever took care to lend him a riding-coat, or a pair of boots, or sometimes a horse of small value, and I always had the satisfaction of finding he never came back to return them.
    Oliver Goldsmith (1728–1774)