Category:Lattice Points

This category contains results about Lattice Points.
Definitions specific to this category can be found in Definitions/Lattice Points.

Let $\R^m$ be the $m$-dimensional real Euclidean space.

Let $\BB = \set {\mathbf v_1, \mathbf v_2, \ldots, \mathbf v_n}$ be a linearly independent set of vectors of $\R^m$.

Let $\LL$ be the point lattice in $\R^m$ whose basis is $\BB$.

Let $\tuple {a_1, a_2, \ldots, a_n}$ be an ordered $n$-tuple of integers.

Let:

$\ds P$

$=$

$\ds \sum_{i \mathop = 1}^n a_i \mathbf v_i$

$\ds $

$=$

$\ds a_1 \mathbf v_1 + a_2 \mathbf v_2 + \cdots + a_n \mathbf v_n$

Then $P$ is a lattice point of $\LL$.

Subcategories

This category has only the following subcategory.