A new semidirect product for association schemes

TL;DR

This paper introduces a novel definition for the semidirect product of association schemes, expanding the theoretical framework and providing a method to construct such products via scheme actions.

Contribution

It generalizes previous work by defining a new semidirect product concept and establishing a construction method using scheme actions.

Findings

Defined a new semidirect product for association schemes

Provided a construction method using scheme actions

Generalized prior work on association scheme products

Abstract

We propose a new definition for the semidirect product of association schemes, generalizing work of Bang, Hirasaka, and Song. We define an action of one scheme on another, and show how one can use such an action to construct all semidirect products satisfying a certain technical condition.