Combinatorial design

Combinatorial design theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties.

Related Topics:
Combinatorial - Mathematics - Systems of finite sets

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

For instance, a balanced incomplete block design (usually called for short a block design) is a collection B of b subsets (called blocks) of a finite set S of v elements, such that any element of X is contained in the same number r of blocks, every block has the same number k of elements, and any two blocks have the same number λ of common elements. For example, if λ = 1, we have a projective plane: X is the point set of the plane and the blocks are the lines.

Related Topics:
Block design - Projective plane

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

A spherical design is a finite set X of points in a (d−1)-dimensional sphere such that, for some integer t, the average value on X of every polynomial

Related Topics:
Spherical design - Sphere

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:f(x1, ..., xd)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

of total degree at most t is equal to the average value of f on the whole sphere, i.e., the integral of f divided by the area of the sphere.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Combinatorial design theory is applied to the design of experiments.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~