Schur rings and non-symmetric association schemes on 64 vertices |
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Authors: | Leif K. Jø rgensen |
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Affiliation: | Aalborg University, Department of Mathematical Sciences, Fr. Bajers Vej 7G, 9220 Aalborg Ø, Denmark |
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Abstract: | In this paper we enumerate essentially all non-symmetric association schemes with three classes, less than 96 vertices and with a regular group of automorphisms. The enumeration is based on a computer search in Schur rings. The most interesting cases have 64 vertices.In one primitive case and in one imprimitive case where no association scheme was previously known we find several new association schemes. In one other imprimitive case with 64 vertices we find association schemes with an automorphism group of rank 4, which was previously assumed not to be possible. |
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Keywords: | Schur ring Non-symmetric association scheme Computer enumeration |
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