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 ?
Bound n-tuples are superposed by addition, and unbinding is performed by an approximate inverse.
Accordingly, (4) is a projective representation of the group of binary n-tuples with addition modulo 2.
bar] E (G) the n-tuple [sigma] (A) is the product of the n-tuples on the edges of A.
n] is identity balanced (or i-balanced), if product of n-tuples on each cycle of [S.
Hence dominant integral weights correspond to weakly decreasing n-tuples of integers, or partitions.
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.
be the constant n-tuples with entries [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
So there is no room to exploit the main resource of the partial isomorphism approach, namely that some n-tuples may neither belong to the extension of a relations, nor to the extension of its negation.
2 An n-ary first-order relation (logical or otherwise) can be regarded as a mapping that maps ordered n-tuples of individuals to truth values.
n] = (G, [sigma]), for any [subset or equal to] E (G) the n-tuple [sigma](A) is the product of the n-tuples on the edges of A.
Each n+1-tuple in this set consists of an individual member of h plus an n-tuple of sets of H-interpretations for the attributed language [L.
1 it suffices to compute the mixed volume Vol ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) for each n-tuple ([A.