Geodesic
Imprimitive cometric association schemes: constructions and analysis
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 4, pp. 399-415.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Dualizing the "extended bipartite double" construction for distance-regular graphs, we construct a new family of cometric (or $Q$-polynomial) association schemes with four associate classes based on linked systems of symmetric designs. The analysis of these new schemes naturally leads to structural questions concerning imprimitive cometric association schemes, some of which we answer with others being left as open problems. In particular, we prove that any $Q$-antipodal association scheme is dismantlable: the configuration induced on any subset of the equivalence classes in the $Q$-antipodal imprimitivity system is again a cometric association scheme. Further examples are explored.
Classification : polynomial, Dedicated, to, the, memory, of, Dom, de, Caen,, 1956-2002
Keywords: keywords association scheme, cometric, $Q$-polynomial, imprimitive, spherical design, linked system of symmetric designs 
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     title = {Imprimitive cometric association schemes: constructions and analysis},
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Martin, William J.; Muzychuk, Mikhail; Williford, Jason. Imprimitive cometric association schemes: constructions and analysis. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 4, pp. 399-415. http://geodesic.mathdoc.fr/item/JAC_2007__25_4_a2/