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Krein conditions and near polygons. (English) Zbl 0738.05025
Author’s summary: “In this article we present a new proof for (and a generalization of) the Krein condition for association schemes. The proof yields necessary and sufficient conditions for the case of equality. In the special case of regular near polygons we give a second matrix-free proof of the special Krein condition \(q_{dd}^ d\geq 0\) and a corresponding characterization of the equality case. Also, Mathon’s inequality for near hexagons is generalized to arbitrary regular near polygons.”.

MSC:
05B30 Other designs, configurations
05E30 Association schemes, strongly regular graphs
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