Enumeration of coherent configurations of order at most 15. (English) Zbl 1427.05233
Summary: This text describes the computerized enumeration of all coherent configurations of order up to 15, and provides some viewpoints of the results of this enumeration. The main discovery resulting from this enumeration is the unique non-Schurian coherent configuration of order 14. We also provide classification of the association schemes of order at most 30 up to algebraic isomorphism, using the classification up to combinatorial isomorphism of those schemes by A. Hanaki and I. Miyamoto [RIMS Kokyuroku 1109, 196–200 (1999; Zbl 0957.05518)].
MSC:
| 05E30 | Association schemes, strongly regular graphs |
| 05A15 | Exact enumeration problems, generating functions |
| 05C30 | Enumeration in graph theory |
| 05C15 | Coloring of graphs and hypergraphs |
Citations:
Zbl 0957.05518Software:
GAPReferences:
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