Combinatorial design.html



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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.

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 X 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.

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

f(x₁, ..., x_d)

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. Some of the basic theory of combinatorial designs originated in Ronald Fisher's work on design of experiments.

External Links

• Design DB: The only database of combinatorial, statistical, experimental block designs

See also

• Kirkman's schoolgirl problem
• Fisher's inequality
• Room square

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