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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.

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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!(nk)!]

2. A method of combining functions in a parallel manner (compare composition). For functions f and g, f : ST and g : UV

the combination f × g is such that f × g : S × UT × V

where S × U and T × V are Cartesian products, and (f × g)(s,u) = (f(s),g(u))

(see ordered pair).

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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.

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a union of people to achieve an aim; a collection of connected ideas, letters, or incidents. See also alliance, coalition.