Infinite family of nonschurian separable association schemes

TL;DR

This paper constructs an infinite family of association schemes that are separable but not Schurian, expanding understanding of the structure and classification of association schemes.

Contribution

It introduces a new infinite family of nonschurian separable association schemes, providing examples that challenge previous assumptions about their classification.

Findings

Constructed an infinite family of nonschurian separable association schemes

Demonstrated the separability of these schemes

Expanded the classification of association schemes

Abstract

An infinite family of nonschurian separable association schemes is constructed.