Jason S. Williford

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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)
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 distanceregular graphs of valency k for each k > 2. That is, we prove that, for any fixed m1 > 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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