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Help on query formulation
Drugs and blocks. (English)
Consortium 2006, No. 91, 7-9 (2006).
Summary: The branch of mathematics that is concerned witn patterns in data ‒ statistics ‒ is critical for making sure that drugs and treatments are effective and safe. What is surprising is that one specialized tool that is used is also a part of combinatorics and geometry. What are block designs or, as they are perhaps more commonly known, BIBDs (Balanced Incomplete Block Design)? We start with a set of objects variously referred to as points or varieties (showing the statistical origins of the idea) denoted by \$V\$, as well as a collection \$B\$ of subsets of \$V\$, called blocks (or lines), all of which have the same number of elements \$k\$. We insist that every element of \$V\$ be contained in exactly \$r\$ blocks and that any pair of elements of \$V\$ lie in exactiy \$λ\$ blocks. The number of elements in \$V\$, \$v\$, and the number elements in \$B\$, \$b\$, as well as \$k\$, \$r\$, and \$λ\$ are called the parameters of the block design. The article presents some very simple examples of BIBDs that illustrate the roots of interest in this subject with geometry.
Classification: M60 G90 K20 N70