faktorimin
Faktorimin is a theoretical construct in combinatorial optimization and factorization theory used to denote the smallest number of factors needed to express a given object under a defined factorization rule. The concept is not tied to a single formal system, but in common formulations it involves a universe U of elements and a collection F of factors (substructures, subsets, or components) such that each element u in U can be represented as a combination (product, sum, or other operation) of a subset of F. A faktorimin of u is a representation of u that uses the smallest possible number of factors.
Formal framework: Given a set U and a family F, and an operation ∘ that combines factors, a
Examples: In a system where factors include both prime and composite components, an element like 12 could
Computation and complexity: Finding a faktorimin can be computationally hard in general, akin to other minimization
Applications: The concept is used as a teaching device to discuss trade-offs in factorization, data compression,
See also: Factorization, Set cover problem, Minimum representation, Factorization system. Notes: Faktorimin is a theoretical construct