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Semilinear set : ウィキペディア英語版
Generalized arithmetic progression

In mathematics, a multiple arithmetic progression, generalized arithmetic progression, ''k''-dimensional arithmetic progression or a linear set, is a set of integers or tuples of integers constructed as an arithmetic progression is, but allowing several possible differences. So, for example, we start at 17 and may add a multiple of 3 ''or'' of 5, repeatedly. In algebraic terms we look at integers
:a + mb + nc + \ldots
where a, b, c and so on are fixed, and m, n and so on are confined to some ranges
:0  ≤  m  ≤  M
and so on, for a finite progression. The number  k, that is the number of permissible differences, is called the ''dimension'' of the generalized progression.
More generally, let
:L(C;P)
be the set of all elements x in N^n of the form
:x = c_0 + \sum_^m k_i x_i,
with c_0 in C, x_1, \ldots, x_m in P, and k_1, \ldots, k_m in N. L is said to be a ''linear set'' if C consists of exactly one element, and P is finite.
A subset of N^n is said to be semilinear if it is a finite union of linear sets.
==See also==

* Freiman's theorem

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Generalized arithmetic progression」の詳細全文を読む



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