multidimensional arithmetic progression

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

	$\displaystyle Q$	$\displaystyle=Q(a;q_{1},\ldots,q_{n};l_{1},\ldots,l_{n})$
		$\displaystyle=\{\,a+x_{1}q_{1}+\cdots+x_{n}q_{n}\mid 0\leq x_{i}<l_{i}\text{ % for }i=1,\ldots,n\,\}.$

The length of the progression is defined as $l_{1}\cdots l_{n}$ . The progression is proper if $|Q|=l_{1}\cdots l_{n}$ .

References

1 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.

Title	multidimensional arithmetic progression
Canonical name	MultidimensionalArithmeticProgression
Date of creation	2013-03-22 13:39:02
Last modified on	2013-03-22 13:39:02
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	7
Author	bbukh (348)
Entry type	Definition
Classification	msc 11B25
Synonym	generalized arithmetic progression
Related topic	ArithmeticProgression