Editing Chromatic polynomial (section)

===Cube method===
There is a natural geometric perspective on graph colorings by observing that, as an assignment of natural numbers to each vertex, a graph coloring is a vector in the integer lattice.
Since two vertices <math>i</math> and <math>j</math> being given the same color is equivalent to the <math>i</math>’th and <math>j</math>’th coordinate in the coloring vector being equal, each edge can be associated with a hyperplane of the form <math>\{x\in\mathbb R^d:x_i=x_j\}</math>. The collection of such hyperplanes for a given graph is called its '''graphic [[arrangement of hyperplanes|arrangement]]'''. The proper colorings of a graph are those lattice points which avoid forbidden hyperplanes.
Restricting to a set of <math>k</math> colors, the lattice points are contained in the cube <math>[0,k]^n</math>. In this context the chromatic polynomial counts the number of lattice points in the <math>[0,k]</math>-cube that avoid the graphic arrangement.