parrelationer

Parrelationer, in this article, are relations that connect two elements to form ordered pairs. Formally, if A and B are sets, a parrelation R from A to B is a subset of A × B; when A = B, R is a parrelation on A. Parrelationer are often described by properties such as left-total (every a ∈ A relates to some b ∈ B), right-total (every b ∈ B is related from some a ∈ A), and functional (each a is related to at most one b). The converse relation R−1 is a parrelation from B to A, and the composition of parrelationer is used in building more complex connections.

Examples include the equality relation on X, consisting of all (x,x), and, in function terms, any function f: A → B is a parrelation that is left-total and functional.

In social sciences, parrelationer describe pairings between individuals, such as dating matches or partnerships, and are analyzed with methods from dyadic data analysis and matching theory. They can be undirected (relations without a distinguished direction) or directed (where the order of the pair matters).

Applications include modeling partnerships, matching problems, data linkage, and the study of interaction patterns in networks.

See also: Binary relation, Graph theory, Matching theory, Function.

References: Standard texts on discrete mathematics and relational models.