Partially Ordered Set - Number of Partial Orders

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:

    Without claiming superiority of intellectual over visual understanding, one is nevertheless bound to admit that the cinema allows a number of æsthetic-intellectual means of perception to remain unexercised which cannot but lead to a weakening of judgment.
    Johan Huizinga (1872–1945)

    The best number for a dinner party is two—myself and a dam’ good head waiter.
    Nubar Gulbenkian (1896–1972)

    Both the man of science and the man of art live always at the edge of mystery, surrounded by it. Both, as a measure of their creation, have always had to do with the harmonization of what is new with what is familiar, with the balance between novelty and synthesis, with the struggle to make partial order in total chaos.... This cannot be an easy life.
    J. Robert Oppenheimer (1904–1967)

    Our own physical body possesses a wisdom which we who inhabit the body lack. We give it orders which make no sense.
    Henry Miller (1891–1980)