The covering radius of permutation designs

TL;DR

This paper investigates the covering radius of permutation designs, specifically t-designs in the symmetric group, deriving bounds based on polynomial zeros and parameters n and t.

Contribution

It introduces upper bounds on the covering radius of permutation designs using properties of Charlier polynomials and parameters n and t.

Findings

Derived upper bounds on the covering radius of t-designs in symmetric groups

Connected the bounds to the largest zeros of Charlier polynomials

Provided a mathematical framework for analyzing permutation design properties

Abstract

A notion of $t$-designs in the symmetric group on $n$ letters was introduced by Godsil in 1988. In particular $t$-transitive sets of permutations form a $t$-design. We derive upper bounds on the covering radius of these designs, as a function of $n$ and $t$ and in terms of the largest zeros of Charlier polynomials.