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Homelattice in $\mathbb{R}^n$

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# lattice in $\mathbb{R}^{n}$

###### Definition.

A lattice in ${\mathbb{R}}^{n}$ is an $n$-dimensional additive free group over $\mathbb{Z}$ which generates ${\mathbb{R}}^{n}$ over $\mathbb{R}$.

Example: The following is an example of a lattice $\mathcal{L}\subset{\mathbb{R}}^{2}$, generated by $w_{1}=(1,2),w_{2}=(4,1)$.

$\mathcal{L}=\{\alpha w_{1}+\beta w_{2}\mid\alpha,\beta\in\mathbb{Z}\}$ |

Defines:

lattice in $\mathbb{R}^n$

Keywords:

lattice, grid

Related:

MinkowskisTheorem, PicksTheorem, ProductOfPosets

Synonym:

lattice, grid

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11H06*no label found*

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## Comments

## Puzzling

I had not followed the thread about \mathbb{C} but this entry (lattice in \mathbb{R}^n) might be having some related trouble. Most puzzling of all, if you look at the bottom of the entry (at least in page images mode) it says "lattice in \sin(x)" is owned by alozano and also in the "also defines: lattice in \sin(x)". However, I never wrote \sin(x) in there and if one sees the entry, it says \mathbb{R}...

What on earth!?

Alvaro

## Re: Puzzling

Hah! This looks like a bug in the inline math rendering system. I'll check it out.

apk

## Re: Puzzling

I fixed this instance, though its likely whatever bug is in the system remains and could crop up again.

apk

## Re: Puzzling

I had seen this before (where an image for a title would get replaced with Â¬sin(x) orsomething else, but it was really sporadic so I thought it was just a cache bug on my side

f

G -----> H G

p \ /_ ----- ~ f(G)

\ / f ker f

G/ker f

## Re: Puzzling

If it *changes* on the same page, it probably *is* a cache bug.

apk