combinationsused

Combinationsused is a term used in combinatorics and computer science to denote the count or tracking of distinct combinations that are generated, examined, or utilized by a process. It is distinct from the mathematical notion of a combination itself, which is a subset of a given size from a set, and from permutations, which consider order.

In algorithmic contexts, combinationsused refers to how many unique combinations a program has produced or inspected. This metric helps quantify computational effort, coverage, or diversity within a search or sampling procedure. For example, when generating 3-element combinations from a 6-element set, there are C(6,3) = 20 possible combinations. If an algorithm stops after processing 7 valid combinations, the value of combinationsused would be 7, even though more combinations exist in theory.

Practical uses include assessing the completeness of enumeration, steering stopping criteria in constraint satisfaction problems, and measuring exploration in heuristics or metaheuristics. It can also aid in avoiding duplicates, ensuring that pruning or filtering steps do not reintroduce previously considered combinations. In design and testing, tracking combinationsused supports reproducibility and fairness by documenting exactly which configurations were evaluated.

Related concepts include the binomial coefficient, combinatorial explosion, enumeration, and coverage. See also combinatorics, algorithm analysis, and sampling methods. Further reading in standard texts on combinatorics and optimization can provide deeper formalization of these ideas.