# On intriguing sets of the Penttila-Williford association scheme

## TL;DR

This paper explores intriguing sets within a specific association scheme, providing examples and characterizations that deepen understanding of their structure and properties.

## Contribution

It introduces new examples and characterizations of intriguing sets in the Penttila-Williford association scheme, advancing knowledge of non-P-polynomial schemes.

## Key findings

- Identification of four types of intriguing sets
- Examples illustrating the structure of these sets
- Characterization results for each type

## Abstract

We investigate intriguing sets of an association scheme introduced by Penttila and Williford (2011) that was the basis for their construction of primitive cometric association schemes that are not $P$-polynomial nor the dual of a $P$-polynomial scheme. In particular, we give examples and characterisation results for the four types of intriguing sets that arise in this scheme.