A Chain Ring Analogue of the Erdos-Ko-Rado Theorem

TL;DR

This paper extends the Erdős-Ko-Rado theorem to intersecting families of subspaces within projective Hjelmslev geometries over finite chain rings, revealing new maximal family structures beyond canonical examples.

Contribution

It introduces a novel analogue of the Erdős-Ko-Rado theorem in the context of projective Hjelmslev geometries over finite chain rings of nilpotency index 2.

Findings

Established an Erdős-Ko-Rado type theorem for these geometries

Provided examples of maximal families that are not canonically intersecting

Extended combinatorial intersection theory to algebraic geometric settings

Abstract

In this paper, we prove an analogue of the Erd\H{o}s-Ko-Rado theorem intersecting families of subspaces in projective Hjelmslev geometries over finite chain rings of nilpotency index 2. We give an example of maximal families that are not canonically intersectng.