Search results
Results from the WOW.Com Content Network
A common type of lattice graph (known under different names, such as grid graph or square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 1, ..., n, y-coordinates being in the range 1, ..., m, and two vertices being connected by an edge whenever the corresponding points are at distance 1.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
A small multiple (sometimes called trellis chart, lattice chart, grid chart, or panel chart) is a series of similar graphs or charts using the same scale and axes, allowing them to be easily compared. It uses multiple views to show different partitions of a dataset.
In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice , or grid lattice.
The hpc lattice (left) and the ccf lattice (right) The principles involved can be understood by considering the most efficient way of packing together equal-sized spheres and stacking close-packed atomic planes in three dimensions. For example, if plane A lies beneath plane B, there are two possible ways of placing an additional atom on top of ...
William Thurston () describes a test for determining whether a simply-connected region, formed as the union of unit squares in the plane, has a domino tiling.He forms an undirected graph that has as its vertices the points (x,y,z) in the three-dimensional integer lattice, where each such point is connected to four neighbors: if x + y is even, then (x,y,z) is connected to (x + 1,y,z + 1), (x ...
Although the original problem asks for integer lattice points in a circle, there is no reason not to consider other shapes, for example conics; indeed Dirichlet's divisor problem is the equivalent problem where the circle is replaced by the rectangular hyperbola. [3]
For topics concerning partially ordered sets with join and meet operations, see Lattice (order) or Category:Lattice theory. Subcategories This category has only the following subcategory.