N-Tuple


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N-Tuple

 

(also ordered n-tuple, cortege), in mathematics, an ordered set of n elements (n is any natural number) called its components or coordinates. Some (or all) components of an n-tuple may coincide. Points (vectors) of an n-dimensional space are often given in terms of n-tuples, namely the ordered sets of their coordinates. Objects that can be described by n independent tests are conveniently characterized by means of n-tuples.

The concept of an n -tuple of numbers plays a fundamental role in the theory of functions of several real variables, and that of an arbitrary n-tuple, in linear algebra (the n-tuples or vectors of linear algebra are a special case of the more general algebraic concept of a matrix), n-tuples are also used, along with other concepts and terms, in mathematical logic, descriptive set theory, topology, functional analysis, the theory of automata, and other branches of mathematics. Basic concepts and formulas of combinatorics are easily and naturally introduced using n-tuples.

IU. A. GASTEV

References in periodicals archive ?
Suppose there exist an n-tuple of strategies [mathematical expression not reproducible] and a trajectory [mathematical expression not reproducible] satisfying (2).
Let J be a distinct-integer N-tuple ([j.sub.1], ..., [j.sub.N]), and let [mathematical expression not reproducible] be the system (11.5), where [[??].sub.p,jl] are the jl-th p-adic w-s motions (11.2), for all l = 1, ..., N.
Indeed the similar conclusions could be obtained for the n-tuple [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we leave the proof for the readers.
An m-repeated low-density burst of length b(fixed) with weight w or less is an n-tuple whose only non-zero components are confined to m distinct sets of b consecutive positions, the first component of each set is non-zero where each set can have at the most w non-zero components (w [less than or equal to] b), and the number of its starting positions in an n-tuple is among the first n - mb + 1 positions.
of real n-tuples or, in 'frequency domain', by component-wise multiplication of (complex) n-tuples,
An n-tuple ([a.sub.1], [a.sub.2], ...,[a.sub.n]) is the identity n-tuple, if [a.sub.k] = +, for 1 [less than or equal to] k [less than or equal to] n, otherwise it is a non-identity n-tuple.
Note that the ambiguity in choosing an n-tuple for the weight [lambda] amounts to an integral translation of GT([lambda]), and hence does not affect its number of integral points.
We write m = [summation over (n/j=1)] [m.sub.j][e.sub.j], where [e.sub.j] is an n-tuple with 1 in the jth position and 0's elsewhere, and we define 0 = (0, ..., 0).
Next, enumerate the elements of S and then, in the usual way, identify each subset of S with an n-tuple of 0's and l's.
A voting pattern is an assignment of a strategy to each participant, in the form of an n-tuple.
A CSP is a triple P = (X, D, C), where X is an n-tuple of variables X = ([x.sub.1], [x.sub.2], ..., [x.sub.n]), D is a corresponding n-tuple of domains D = ([D.sub.1], [D.sub.2], ..., [D.sub.n]) such that [x.sub.i] [member of] [D.sub.i], and C is a f-tuple of constraints C = ([C.sub.1], [C.sub.2],...., [C.sub.t]).
An n-tuple ([a.sub.1], [a.sub.2], ..., [a.sub.n]) is symmetric, if [a.sub.k] = [a.sub.n-k+1], 1 [less than or equal to] k [less than or equal to] n.