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Association schemes of small order

✍ Scribed by Kyoungah See; Sung Y. Song

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
531 KB
Volume
73
Category
Article
ISSN
0378-3758

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✦ Synopsis

We survey the work on the classiΓΏcation problem of association schemes of small order. Our aim is to introduce some construction methods which simplify the description of known schemes, and provide the complete catalogue of all association schemes for a given order n, where n = 4; 5; : : : ; 15. Part of this work deals with the construction and enumeration of association schemes via Schur rings and two ways of tensoring association matrices; another part deals with the fusion relation of association schemes of a given order by using the notion of the wreath product and direct product of association schemes. The association schemes are presented in Hasse diagrams of partially ordered sets under the fusion relations. Our list includes, in particular, all symmetric association schemes, the source of partially balanced incomplete block designs with the corresponding number of treatments.

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