On separability of Tatra association schemes

TL;DR

This paper proves that Tatra association schemes, derived from symmetric bilinear forms on finite field vector classes, are uniquely determined by their 2-dimensional intersection numbers.

Contribution

It establishes that all Tatra association schemes are 2-separable, a property previously unconfirmed for this class.

Findings

Every Tatra association scheme is 2-separable.

Tatra schemes are determined by their 2-dimensional intersection numbers.

Abstract

A Tatra association scheme is an association scheme arising from a symmetric bilinear form defined on the equivalence classes of nonzero $2$-dimensional vectors modulo some subgroup of the multiplicative group of a finite field. In the present paper, we prove that every such association scheme is $2$-separable, i.e. it is determined up to isomorphism by the tensor of its $2$-dimensional intersection numbers.