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 ?
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.
A 2-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 two 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 - 2b + 1 positions.
n] = (G, [sigma]) is i-balanced if, and only if, it is possible to assign n-tuples to its vertices such that the n-tuple of each edge uv is equal to the product of the n-tuples of u and v.
n] defined as follows: each vertex v [member of] V, [micro](v) is the n-tuple which is the product of the n-tuples on the edges incident with v.
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 identify a weight [lambda] with the n-tuple ([[lambda].
j] is an n-tuple with 1 in the jth position and 0's elsewhere, and we define 0 = (0, .
n] defined as follows: each vertex v [member of] V, [mu](v) is the n-tuple which is the product of the n-tuples on the edges incident with v.
n] with respect to [mu] is the operation of changing the n-tuple of every edge uv of [S.
The algebra of the logical exclusive or (xor) operation applied to ordered n-tuples of true (T) and false (F) is an example of an AC-algebra.
of real n-tuples or, in 'frequency domain', by component-wise multiplication of (complex) n-tuples,
Bound n-tuples are superposed by addition, and unbinding is performed by an approximate inverse.