In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application. These applications come from many areas, including experimental design, finite geometry, software testing, cryptography, and algebraic geometry. Many variations have been examined, but the most intensely studied are the balanced incomplete block designs (BIBDs or 2-designs) which historically were related to statistical issues in the design of experiments.
A block design in which all the blocks have the same size is called uniform. The designs discussed in this article are all uniform. Pairwise balanced designs (PBDs) are examples of block designs that are not necessarily uniform.
Read more about Block Design: Definition of A BIBD (or 2-design), Symmetric BIBDs, Resolvable 2-designs, Generalization: t-designs, Steiner Systems, Partially Balanced Designs (PBIBDs), Applications
Famous quotes containing the words block and/or design:
“Only he who can view his own past as an abortion sprung from compulsion and need can use it to full advantage in the present. For what one has lived is at best comparable to a beautiful statue which has had all its limbs knocked off in transit, and now yields nothing but the precious block out of which the image of one’s future must be hewn.”
—Walter Benjamin (1892–1940)
“I begin with a design for a hearse.
For Christ’s sake not black—
nor white either—and not polished!
Let it be weathered—like a farm wagon—”
—William Carlos Williams (1883–1963)