Bijekns

Bijekns is a term used in theoretical computer science and mathematics to denote a class of structure-preserving bijections between two domains, augmented by a constraint that preserves a designated relation R. In a typical Bijekn, there is a pair of functions f: A → B and g: B → A such that f and g are inverses, and for all elements a1, a2 in A, R(a1, a2) if and only if R(f(a1), f(a2)). This makes Bijekns a reversible, relation-preserving correspondence between A and B.

Developed to model interoperable transformations, Bijekns allow researchers to transfer properties across domains without violating relational structure. They generalize ordinary bijections by requiring that the chosen relation R be invariant under forward and backward mapping. When R encodes equality or a fixed equivalence, Bijekns reduce to standard isomorphisms between structures; for more complex relations they enable analysis of how relational constraints survive transformation.

Origin and usage: The concept originated in the early 2020s within discussions on data integration and formal verification of system equivalence. While primarily explored in theoretical contexts, Bijekns have seen practical applications in schema mapping, model checking, and reversible computing, where maintaining relational integrity during data or state transfer is important. Extensions include partial Bijekns, defined on subdomains, and probabilistic Bijekns, where f and g are random but constrained bijections.

See also: bijection, isomorphism, permutation, relation, data transformation, schema mapping.