structural:expansion
Strict partial orders

An irreflexive, strong, or strict partial order is a homogeneous relation < on a set P {\displaystyle P} that is irreflexive, asymmetric, and transitive; that is, it satisfies the following conditions for all a, b, c ∈ P: {\displaystyle a,b,c\in P:}

Irreflexivity and transitivity together imply asymmetry. Also, asymmetry implies irreflexivity. In other words, a transitive relation is asymmetric if and only if it is irreflexive. So the definition is the same if it omits either irreflexivity or asymmetry (but not both).

A strict partial order is also known as an asymmetric strict preorder.