On the uniqueness of the tetrahedral association schemes

Let V be the set of (₃⁴) 3- sets in {1 … n}. Say p, q ∈ V are ith associates, (p, q) ∈ A_i, if 3 = i + |p ∩ q|. An association scheme is tetrahedral if it is isomorphic to the scheme {A₀, A₁, A₂, A₃} and a graph is tetrahedral if it is isomorphic to A₁. Aigner 1] and Bose and Laskar 2] have shown that the tetrahedral graphs are characterized by their characteristic equations, provided n < 9 or n > 16. The present paper extends methods of Hoffman 7] to show that the tetrahedral association schemes are characterized by their structural constants, provided n > 10.