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:
“Today, almost forty years later, I grow dizzy when I recall that the number of manufactured tanks seems to have been more important to me than the vanished victims of racism.”
—Albert Speer (1905–1981)
“After a certain number of years our faces become our biographies. We get to be responsible for our faces.”
—Cynthia Ozick (b. 1928)
“We were soon in the smooth water of the Quakish Lake,... and we had our first, but a partial view of Ktaadn, its summit veiled in clouds, like a dark isthmus in that quarter, connecting the heavens with the earth.”
—Henry David Thoreau (1817–1862)
“Your money’s no good here. Orders of the house.”
—Stanley Kubrick (b. 1928)