On the Uniqueness of the Triangular Association Scheme

Abstract

Connor [3] has shown that the relations among the parameters of the triangular association scheme themselves imply the scheme if $n \geqq 9$. This result was shown by Shrikhande [6] to hold also if $n \leqq 6$. (The problem has no meaning for $n < 4$.) This paper shows that the result holds if $n = 7$, but that it is false if $n = 8$.