combination

a. the set of numbers that opens a combination lock

b. the mechanism of this type of lock

2. Brit a motorcycle with a sidecar attached

3. Maths

a. an arrangement of the numbers, terms, etc., of a set into specified groups without regard to order in the group

b. a group formed in this way. The number of combinations of n objects taken r at a time is n!/[(n -- r)!r!]. Symbol: _nC_r

4. the chemical reaction of two or more compounds, usually to form one other compound

5. Chess a tactical manoeuvre involving a sequence of moves and more than one piece

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

combination

[‚käm·bə′nā·shən]

(mathematics)

A selection of one or more of the elements of a given set without regard to order.

combination

(mathematics)

A set containing a certain number of objects selected from another set.

The number of combinations of r objects chosen from a set of n is

n C r = n! / ((n-r)! r!)

where "n C r" is normally with n and r as subscripts or as n above r in parentheses.

See also permutation.

combination

(reduction)

In the theory of combinators, a combination denotes an expression in which function application is the only operation.

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Combination

(in Russian, kombinatsiia). (1) An interdependent union, connection, or arrangement of several objects or component parts (elements) of a single object.

(2) A set of procedures for carrying out a complex plan, such as a chess combination.

(3) A contrivance, trick, or subterfuge; a deliberate maneuver to achieve a mercenary or other improper goal (commercial combination; political combination).

(4) An item of women’s underclothing (a slip).

Combination

in mathematics. Combinations of n elements taken k at a time are sets that contain k of the n elements and that differ from each other in at least one element. The number of combinations of n elements, k at a time, is denoted by , C (n, k), or and is equal to n!/k!(n - k)! (seeCOMBINATORICS).

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References in periodicals archive

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Many different adversaries are considered, motivated by differences in eavesdropping technologies, We characterize the feasibility of the two privacy tasks combinatorially, construct protocols for the feasible cases, and analyze their computational complexity.

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This automation saves human negotiation time, and computational agents are often better at finding deals in combinatorially and strategically complex settings.

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In the case of multidimensional variation, this approach breaks down because the number of branches explodes combinatorially. Let us assume that each dimension is modeled by an attribute with domain [A.sub.i].

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So if the piece was twelve-tone, which seemed likely due to its sound and texture - not to mention that all the other pieces of Swift's I knew were twelve-tone - either it would not be combinatorially aggregate-forming (as in Webern or Berg) or it would use weighted aggregates and/or super-arrays (as in Babbitt).

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Truth tables, for example, are based on the hidden convention of combinatorially assigning truth values according the principles of noncontradiction and excluded middle.

Conventions, cognitivism and necessity

Terms that are combinatorially vague are vague by virtue of the apparent indeterminacy surrounding what to count as the set of necessary and sufficient conditions, regardless of whether or not the considered conditions themselves are vague.

Vagueness