# Note on the diversity of intersecting families

## TL;DR

This paper constructs two intersecting families with higher diversity than a certain sum, disproving Huang's conjecture for odd n=2k+1 with k≥3.

## Contribution

It provides explicit examples of intersecting families with greater diversity, challenging previous conjectures in combinatorics.

## Key findings

- Disproved Huang's conjecture for odd n=2k+1 with k≥3.
- Constructed two intersecting families with higher diversity than the specified sum.
- Enhanced understanding of the diversity properties of intersecting families.

## Abstract

Let $n=2k+1$ be odd with $k\geq3$. In this note, we give two intersecting families with diversity larger than $\sum_{i=k+1}^{2k} \binom {2k}{i}$, which disprove a conjecture of Huang.