Relations among partitions

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Abstract

Combinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.
Original languageEnglish
Title of host publicationSurveys in Combinatorics 2017
EditorsAnders Claesson, Mark Dukes, Sergey Kitaev, David Manlove, Kitty Meeks
Place of PublicationCambridge
PublisherCambridge University Press
Pages1-86
Number of pages86
ISBN (Electronic)9781108332699
ISBN (Print)9781108413138
DOIs
Publication statusPublished - 2017

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
Volume440
ISSN (Print)0076-0552

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