Association schemes of small order
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- 作者：See ; Kyoungah ; et. al.
- 关键词：05E30 ; 05B99 ; Bose&ndash ; Mesner algebra ; Cellular rings ; Centralizer rings ; Fusion schemes and fission schemes ; Kronecker-product ; Partially ordered sets ; Schur rings
- 刊名：Journal of Statistical Planning and Inference
- 出版年：1998
- 出版时间：September 1, 1998
- 年：1998
- 卷：73
- 期：1-2
- 页码：225-271
- 全文大小：531 K
文摘
We survey the work on the classification 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.