Number of Partial Orders
Sequence A001035 in OEIS gives the number of partial orders on a set of n labeled elements:
| 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 |
The number of strict partial orders is the same as that of partial orders.
If we count only up to isomorphism, we get 1, 1, 2, 5, 16, 63, 318, … (sequence A000112 in OEIS).
Read more about this topic: Partially Ordered Set
Famous quotes containing the words number of, number, partial and/or orders:
“I heartily wish you, in the plain home-spun style, a great number of happy new years, well employed in forming both your mind and your manners, to be useful and agreeable to yourself, your country, and your friends.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“The serial number of a human specimen is the face, that accidental and unrepeatable combination of features. It reflects neither character nor soul, nor what we call the self. The face is only the serial number of a specimen.”
—Milan Kundera (b. 1929)
“The one-eyed man will be King in the country of the blind only if he arrives there in full possession of his partial faculties—that is, providing he is perfectly aware of the precise nature of sight and does not confuse it with second sight ... nor with madness.”
—Angela Carter (1940–1992)
“One cannot be a good historian of the outward, visible world without giving some thought to the hidden, private life of ordinary people; and on the other hand one cannot be a good historian of this inner life without taking into account outward events where these are relevant. They are two orders of fact which reflect each other, which are always linked and which sometimes provoke each other.”
—Victor Hugo (1802–1885)