We show the existence of a four-class association scheme defined on the unordered pairs of distinct points from PG(1, q(2)), for q greater than or equal to 4 a power of 2, thereby proving a conjecture of D. de Caen and E. van Darn (Fissioned triangular schemes via the cross-ratio, European J. Combin. 22 (2001), 297-301). This is a fusion of certain relations in the fission scheme FT(q(2) + 1) obtained from the triangular association scheme. Combining three relations in the above four-class association scheme yields a strongly regular graph, which we show is isomorphic to one constructed by Brouwer and Wilbrink using hyperbolic solid sections of the parabolic quadric in PG(4, q). (C) 2001 Academic Press. [References: 7]
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机译：我们显示存在一个四类关联方案，该方案定义于PG（1，q（2））的不同点的无序对上，其中q大于或等于4的2的幂，从而证明了D的猜想。 de Caen和E.van Darn（通过交叉比率进行裂变三角形方案，欧洲J. Combin。22（2001），297-301）。这是从三角关联方案获得的裂变方案FT（q（2）+1）中某些关系的融合。在上述四类关联方案中组合三个关系会产生一个强正则图，我们展示了它与Brouwer和Wilbrink使用PG（4，q）中抛物二次曲面的双曲实心部分构造的同构图。 （C）2001学术出版社。 [参考：7]
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