The exchange condition for association schemes
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The present article generalizes the group-theoretical exchange condition to the theory of association schemes. We prove that a large class of association schemes satisfying our exchange condition arises from groups as quotients over subgroups. The result provides an alternate proof of Tits' reduction theorem for buildings of spherical type.
KeywordsExchange Condition Coxeter Group Association Scheme Reduction Theorem Spherical Type
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- I. A. Faradzev, M. H. Klin and M. E. Muzichuk,Cellular rings and groups of automorphisms of graphs, inInvestigations in Algebraic Theory of Combinatorial Objects (I. A. Faradzev, A. A. Ivanov, M. H. Klin and A. Woldar, eds.), Kluwer Academic Publishers, Dordrecht, 1994, pp. 1–152.CrossRefGoogle Scholar