The covering radius of permutation designs (2108.04275v1)

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.