Divisible Designs, Laguerre Geometry, and Beyond

TL;DR

This paper explores the connections between divisible designs and Laguerre geometry within the context of projective geometry over rings, aiming to unify and clarify their interaction for further research.

Contribution

It provides an overview and initial development of the relationship between design theory and projective geometry over rings, highlighting key connections and suggesting directions for future study.

Findings

Established foundational links between divisible designs and Laguerre geometry.

Presented basic concepts and their interactions in a unified framework.

Recommended further reading and research directions.

Abstract

In these notes we aim at bringing together design theory and projective geometry over a ring. Both disciplines are well established, but the results on the interaction between them seem to be rare and scattered over the literature. Thus our main goal is to present the basics from either side, to develop, or at least sketch, the principal connections between them, and to make recommendations for further reading. There is no attempt to provide encyclopedic coverage with expansive notes and references.