A note on Erd\"os-Ko-Rado sets of generators in Hermitian polar spaces

TL;DR

This paper improves the upper bound on the size of Erdős-Ko-Rado sets of generators in certain Hermitian polar spaces, specifically when the dimension is odd and at least 5, using a variant of Hoffman's bound.

Contribution

It provides a tighter upper bound for Erdős-Ko-Rado sets in Hermitian polar spaces where the maximum was previously unknown.

Findings

New upper bound established for specific Hermitian polar spaces.

Enhanced understanding of combinatorial structures in finite classical polar spaces.

Application of Hoffman's bound variant to geometric combinatorics.

Abstract

The size of the largest Erd\H os-Ko-Rado set of generators in the finite classical polar space is known for all polar spaces except for $H(2d-1,q^2)$ when $d\ge 5$ is odd. We improve the known upper bound in this remaining case by using a variant of the famous Hoffman's bound.