The second largest Erd\H{o}s-Ko-Rado sets of generators of the hyperbolic quadrics $\mathcal{Q}^{+}(4n+1,q)$

TL;DR

This paper classifies the second largest maximal Erdős-Ko-Rado sets of generators in hyperbolic quadrics (4n+1,q) for q  3, advancing understanding of combinatorial structures in finite geometry.

Contribution

It provides a complete classification of the second largest Erd46s-Ko-Rado sets of generators in hyperbolic quadrics (4n+1,q), a previously unresolved problem.

Findings

Identified the second largest maximal Erd46s-Ko-Rado sets.

Classified these sets explicitly for q  3.

Enhanced understanding of combinatorial configurations in hyperbolic quadrics.

Abstract

An Erd\H{o}s-Ko-Rado set of generators of a hyperbolic quadric is a set of generators which are pairwise not disjoint. In this article we classify the second largest maximal Erd\H{o}s-Ko-Rado set of generators of the hyperbolic quadrics $\mathcal{Q}^{+}(4n+1,q)$, $q\geq3$.