Strict partial order

A binary relation that is irreflexive and transitive. It orders some pairs of elements while allowing others to remain incomparable.

Binary relation: A relation between elements of two sets, represented as a set of ordered pairs. A strict partial order is a binary relation on a set.
Transitive closure: The smallest transitive relation containing a given relation. It adds all precedence implied by chains in the original relation.
Strict total order: An irreflexive, transitive relation that compares every pair of distinct elements in exactly one direction. Unlike a strict partial order, it leaves no distinct pair incomparable.
Task scheduling: The allocation and sequencing of tasks subject to resource limits and precedence constraints. A task must precede another when the order relates their completion requirements.
Irreflexivity: A relation is irreflexive when no element is related to itself. This condition rules out every self-comparison in a strict partial order.
Topological sorting: A linear ordering of a directed acyclic graph's vertices that places each source before its targets. It turns the order's precedence constraints into one compatible sequence.
Partial order: A reflexive, antisymmetric, transitive relation that may leave distinct elements incomparable. It expresses the non-strict counterpart through reflexive comparisons.
Dependency graph: A directed graph whose edges record that one item depends on another. Reachability in an acyclic dependency graph defines a strict partial order.
Transitivity: A relation is transitive when x related to y and y related to z imply x related to z. Transitivity carries strict precedence through chains of related elements.
Linear extension: A total order that preserves every comparison in a given partial order. Each linear extension completes the strict partial order's otherwise incomparable pairs.

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