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multidimensional arithmetic progression (Definition)

An $n$ -dimensional arithmetic progresssion is a set of the form

$\displaystyle Q$ $\displaystyle =Q(a; q_1, \dotsc, q_n; l_1, \dotsc, l_n)$    
  $\displaystyle =\{\,a+x_1 q_1+\dotsb+x_n q_n \mid 0\leq x_i<l_i$ for $\displaystyle i=1,\dotsc,n \,\}.$    

The length of the progression is defined as $ l_1\dotsb l_n$ . The progression is proper if $ \vert Q\vert=l_1\dotsb l_n$ .

References

1
Melvyn B. Nathanson.
Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM.
Springer, 1996.
Zbl 0859.11003.



"multidimensional arithmetic progression" is owned by bbukh.
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See Also: arithmetic progression

Other names:  generalized arithmetic progression
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Cross-references: length, arithmetic
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This is version 4 of multidimensional arithmetic progression, born on 2003-05-26, modified 2004-01-25.
Object id is 4303, canonical name is MulidimensionalArithmeticProgression.
Accessed 4166 times total.

Classification:
AMS MSC: 11B25 (Number theory :: Sequences and sets :: Arithmetic progressions)
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