Association schemes in which the thin residue is an elementary abelian $p$-group of rank $2$

TL;DR

This paper explores the existence and schurity of association schemes with thin residues isomorphic to an elementary abelian p-group of rank 2, contributing to the understanding of their structural properties.

Contribution

It investigates the conditions under which such association schemes exist and are schurian, focusing on the case where the thin residue is an elementary abelian p-group of rank 2.

Findings

Characterization of association schemes with specified thin residue

Conditions for schurity of these schemes

Insights into their structural properties

Abstract

In this article, we investigate the existence and schurity problem of association schemes whose thin residues are isomorphic to an elementary abelian $p$-group of rank $2$.