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A Four-Class Association Scheme

โœ Scribed by Gary L. Ebert; Sebastian Egner; Henk D.L. Hollmann; Qing Xiang

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
131 KB
Volume
96
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

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 4 a power of 2, thereby proving a conjecture of D. de Caen and E. van Dam (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).

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โœ Hajime Tanaka ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 103 KB

## HAJIME TANAKA Let denote the set of two-element subsets of the projective line P G(1, q), where q = 2 e , e โ‰ฅ 1. The character table of the association scheme X(P G L(2, q), ) is calculated. Then by using this character table, we prove that the conjectured subscheme of de Caen and van Dam is in