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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
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