Homogeneous relation

Common types of endorelations include orders, graphs, and equivalences.

Some particular homogeneous relations over a set X (with arbitrary elements x1, x2) are: Fifteen large tectonic plates of the Earth's crust contact each other in a homogeneous relation.

Some important properties that a homogeneous relation R over a set X may have are: The previous 6 alternatives are far from being exhaustive; e.g., the binary relation xRy defined by y = x2 is neither irreflexive, nor coreflexive, nor reflexive, since it contains the pair (0, 0), and (2, 4), but not (2, 2), respectively.

Again, the previous 3 alternatives are far from being exhaustive; as an example over the natural numbers, the relation xRy defined by x > 2 is neither symmetric nor antisymmetric, let alone asymmetric.

A strict partial order, also called strict order,[citation needed] is a relation that is irreflexive, antisymmetric, and transitive.

It is also a relation that is symmetric, transitive, and total, since these properties imply reflexivity.

[16] The number of distinct homogeneous relations over an n-element set is 2n2 (sequence A002416 in the OEIS): Note that S(n, k) refers to Stirling numbers of the second kind.