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On Primitive Commutative Association Schemes with a Nonsymmetric Relation of Valency 4

✍ Scribed by Mitsugu Hirasaka

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 168 KB
Volume: 219
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7873

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✦ Synopsis

Let X, G be a primitive commutative association scheme. If g g G is nonsym-Ž . metric of valency 4, then the graph X, g is uniquely determined up to isomorphism. In particular, the cardinality of X is the cube of an odd prime. ᮊ 1999

X

Let r : X = X be given. We set < r* [ x, y y, x g r , Ä 4 Ž . Ž .

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Primitive Commutative Association Scheme

Primitive Commutative Association Schemes with a Non-symmetric Relation of Valency 3

✍ Mitsugu Hirasaka 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 247 KB

Let (X, [R i ] 0 i d ) be a primitive commutative association scheme. If there is a non-symmetric relation R i with valency 3, then the cardinality of X is equal to either p or p 2 where p is an odd prime. Moreover, if |X | = p then (X, [R i ] 0 i d ) is isomorphic to a cyclotomic scheme.