com·bi·na·tion / ˌkämbəˈnāshən/ • n. 1. the act or an instance of combining; the process of being combined. ∎ [as adj.] uniting different uses, functions, or ingredients: a combination garment bag and backpack. ∎ the state of being joined or united in such a way: these four factors work together in combination. ∎ Chem. the joining of substances in a compound with new properties. ∎ Chem. the state of being in a compound. 2. a set of people or things that have been combined: a combination of beauty and utility. ∎ an arrangement of elements: the canvases may be arranged in any number of combinations. ∎ a sequence of numbers or letters used to open a combination lock. ∎ (in various sports and games) a coordinated and effective sequence of moves. ∎ (in equestrian sports) a jump consisting of two or more elements. 3. Math. a selection of a given number of elements from a larger number without regard to their arrangement. DERIVATIVES: com·bi·na·tion·al / -shənl/ adj. com·bi·na·tive / ˈkämbəˌnātiv; kəmˈbīnətiv/ adj. com·bi·na·to·ri·al / ˌkämbənəˈtôrēəl; kəmˌbīnə-/ adj. ( Math. ) com·bi·na·to·ri·al·ly adv. ( Math. ) com·bi·na·to·ry / kəmˈbīnəˌtôre; ˈkämbənə-/ adj.
1. A subset of a finite set of elements. The number of combinations of n distinct objects taken k at a time is nCk = n!/[k!(n–k)!]
2. A method of combining functions in a parallel manner (compare composition). For functions f and g, f : S → T and g : U → V
the combination f × g is such that f × g : S × U → T × V
where S × U and T × V are Cartesian products, and (f × g)(s,u) = (f(s),g(u))
(see ordered pair).
Incriminal law, an agreement between two or more people to act jointly for an unlawful purpose; a conspiracy. In patent law, the joining together of several separate inventions to produce a new invention.
An illegal combination in restraint of trade, defined under the sherman anti-trust act, is one in which the conspirators agree expressly or impliedly to use devices such as price-fixing agreements to eliminate competition in a certain locality, e.g., when a group of furniture manufacturers refuse to deliver goods to stores that sell their goods for under a certain price.
In patent law a combination is distinguishable from an aggregation in that it is a joint operation of elements that produces a new result as opposed to a mere grouping together of old elements. This is important in determining whether or not something is patentable, since no valid patent can extend to an aggregation.