The covering radius of permutation designs

DOI10.1007/S10801-022-01169-4arXiv2108.04275MaRDI QIDQ6374865

Patrick Solé

Publication date: 9 August 2021

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.

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Other designs, configurations (05B30) Permutation groups (20B99)

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