The covering radius of permutation designs

08/09/2021

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by   Patrick Solé, et al.

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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.