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 ?
Accordingly, (4) is a projective representation of the group of binary n-tuples with addition modulo 2.
c] model and BSC are based on two different representations (in group theoretical sense) of the additive group of binary n-tuples with addition modulo 2.
Atomic objects are real-valued vectors in n-dimensional Euclidean space, in practice represented by n-tuples of components taken in some basis.
n] is identity balanced (or i-balanced), if product of n-tuples on each cycle of [S.
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.
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.
to be the constant n-tuple with entry [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
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.
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.