Relations among partitions
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.
Citation
Bailey , R A 2017 , Relations among partitions . in A Claesson , M Dukes , S Kitaev , D Manlove & K Meeks (eds) , Surveys in Combinatorics 2017 . London Mathematical Society Lecture Note Series , vol. 440 , Cambridge University Press , Cambridge , pp. 1-86 . https://doi.org/10.1017/9781108332699.002
Publication
Surveys in Combinatorics 2017
Status
Peer reviewed
ISSN
0076-0552Type
Book item
Rights
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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