Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids.
Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry, tournament scheduling, lotteries, mathematical chemistry, mathematical biology, algorithm design and analysis, networking, group testing and cryptography.[1]
^Stinson 2003, pg.1
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Combinatorialdesign theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets...
combinatorics. Combinatorialdesign theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated...
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such...
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analysis, and optimization; for the design of experiments, statisticians use algebra and combinatorialdesign. Applied mathematicians and statisticians...
Raghavarao, Damaraju (1971). "Weighing Designs". Constructions and combinatorial problems in design of experiments. New York: Wiley. pp. 305–308. ISBN 978-0471704850...
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