Resolved designs viewed as sets of partitions
نویسنده
چکیده
In this paper I take the view, common among statisticians, that a design is an allocation of a set Γ of n treatments to a set Ω of plots: see [2]. (The word plot does not necessarily denote a piece of ground: it is used for any type of experimental unit.) Thus the design may be thought of as a function f from Ω onto Γ: plot ω receives treatment γ if f(ω) = γ. If Ω is partitioned into blocks then f is called a block design. A block design is proper if all its blocks have the same size. In this paper all block designs are proper, having b blocks of size k. Suppose that the restriction of f to each block is injective, that is,
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