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:
“The chess pieces are the block alphabet which shapes thoughts; and these thoughts, although making a visual design on the chess-board, express their beauty abstractly, like a poem.... I have come to the personal conclusion that while all artists are not chess players, all chess players are artists.”
—Marcel Duchamp (1887–1968)
“Westerners inherit
A design for living
Deeper into matter—
Not without due patter
Of a great misgiving.”
—Robert Frost (1874–1963)