Linked systems of symmetric group divisible designs

TL;DR

This paper introduces linked systems of symmetric group divisible designs, explores their connection to association schemes, and provides bounds and examples, advancing combinatorial design theory.

Contribution

It defines linked systems of symmetric group divisible designs, establishes their connection with association schemes, and derives an upper bound on their number.

Findings

Established a connection with association schemes

Derived an upper bound on linked systems

Provided examples of linked systems

Abstract

We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which are linked. Several examples of linked systems of symmetric group divisible designs are provided.