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:
“I think, for the rest of my life, I shall refrain from looking up things. It is the most ravenous time-snatcher I know. You pull one book from the shelf, which carries a hint or a reference that sends you posthaste to another book, and that to successive others. It is incredible, the number of books you hopefully open and disappointedly close, only to take down another with the same result.”
—Carolyn Wells (1862–1942)
“I will not adopt that ungenerous and impolitic custom so common with novel writers, of degrading by their contemptuous censure the very performances, to the number of which they are themselves adding—joining with their greatest enemies in bestowing the harshest epithets on such works, and scarcely ever permitting them to be read by their own heroine, who, if she accidentally take up a novel, is sure to turn over its insipid leaves with disgust.”
—Jane Austen (1775–1817)
“Consciousness, we shall find, is reducible to relations between objects, and objects we shall find to be reducible to relations between different states of consciousness; and neither point of view is more nearly ultimate than the other.”
—T.S. (Thomas Stearns)