Non-trivial intersecting families for finite affine spaces

TL;DR

This paper characterizes the largest non-trivial intersecting families in finite affine spaces, extending understanding beyond trivial solutions and identifying the structure of these maximal families.

Contribution

It provides a complete characterization of maximum-sized non-trivial intersecting families in finite affine spaces, a previously unresolved problem.

Findings

Identified the structure of maximum non-trivial intersecting families

Extended the classification beyond trivial solutions

Provided theoretical bounds for such families

Abstract

Guo and Xu determined the maximum size of intersecting families over finite affine spaces and showed that any family reaches maximum size must be trivial. In this paper, we characterize non-trivial intersecting family with maximum size.