Block design

From Groupprops
Jump to: navigation, search

Definition

Definition with symbols

A (v,k,\lambda)-block design is the following data:

  • A set S with v elements, called the vertices
  • A collection of k-element subsets of S, called blocks. The number of blocks is denoted as b

Satisfying the following conditions:

  • Every point is contained in the same number of blocks (this is denoted as r)
  • Given any two points, the number of blocks containing both of them is \lambda
Note that b and r are dependent on the other three parameters via some obvious relations PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

This is also called a BIBD or a Balanced Incomplete Block Design.

Further definition

A generalization of block design is to t-block design. A t-block design has the property that for any t elements, the number of blocks cotaining all t of them is fixed and independent of the choice of elements. Such a thing is called, in more detail, a t-(v,k,\lambda) block design.