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On Quasi-thin Association Schemes

โœ Scribed by Mitsugu Hirasaka; Mikhail Muzychuk

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
144 KB
Volume
98
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

An association scheme (or simply, a scheme) is called thin if each of its basic relations has valency 1. It is easy to see that thin schemes can be viewed as groups and, conversely, groups can be seen as thin schemes. In the present paper, we investigate schemes the basic relations of which have valency 1 or 2. We call these schemes quasi-thin. In order to formulate our results we let (X, R) denote a scheme (in the sense of P.-H. Zieschang). We first offer three sufficient conditions for (X, R) to have an automorphism group acting transitively on X. These conditions are

R possesses an element r such that OrP=R and Orr g P=Or g rP. We then prove that, if , 4, 7, 8, 12, 16}. As a consequence of the latter result, we obtain a classification of the quasi-thin schemes with |X|=4p, where p is a prime number.

๐Ÿ“œ SIMILAR VOLUMES

On Quasi-thin Association Schemes with O
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