Relations among partitions

Rosemary Anne Bailey

doi:10.1017/9781108332699.002

Relations among partitions

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

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 language	English
Title of host publication	Surveys in Combinatorics 2017
Editors	Anders Claesson, Mark Dukes, Sergey Kitaev, David Manlove, Kitty Meeks
Place of Publication	Cambridge
Publisher	Cambridge University Press
Pages	1-86
Number of pages	86
ISBN (Electronic)	9781108332699
ISBN (Print)	9781108413138
DOIs	https://doi.org/10.1017/9781108332699.002
Publication status	Published - 2017

Publication series

Name	London Mathematical Society Lecture Note Series
Publisher	Cambridge University Press
Volume	440
ISSN (Print)	0076-0552

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10.1017/9781108332699.002

Bailey_2017_Relations_Surveys_LMSLNS_AAM
Copyright © 2017, Cambridge University Press. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/9781108332699.002
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Relations among partitions. / Bailey, Rosemary Anne.
Surveys in Combinatorics 2017. ed. / Anders Claesson; Mark Dukes; Sergey Kitaev; David Manlove; Kitty Meeks. Cambridge: Cambridge University Press, 2017. p. 1-86 (London Mathematical Society Lecture Note Series; Vol. 440).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

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Relations among partitions

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