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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… (More)

- William J. Martin, Jason S. Williford
- Eur. J. Comb.
- 2009

In this paper, we will prove a result which is formally dual to the long-standing conjecture of Bannai and Ito which claims that there are only finitely many distance-regular graphs of valency k for each k > 2. That is, we prove that, for any fixed m 1 > 2, there are only finitely many cometric association schemes (X, R) with the property that the first… (More)

In a recent paper [9], the authors introduced the extended Q-bipartite double of an almost dual bipartite cometric association scheme. Since the association schemes arising from linked systems of symmetric designs are almost dual bipartite, this gives rise to a new infinite family of 4-class cometric schemes which are both Q-bipartite and Q-antipodal. These… (More)

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