Covering radius in the Hamming permutation space

Kevin Hendrey, Ian M. Wanless

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1 Citation (Scopus)

Abstract

Let Sn denote the set of permutations of {1,2,…,n}. The function f(n,s) is defined to be the minimum size of a subset S⊆Sn with the property that for any ρ∈Sn there exists some σ∈S such that the Hamming distance between ρ and σ is at most n−s. The value of f(n,2) is the subject of a conjecture by Kézdy and Snevily, which implies several famous conjectures about Latin squares. We prove that the odd n case of the Kézdy–Snevily Conjecture implies the whole conjecture. We also show that f(n,2)>3n∕4 for all n, that s!<f(n,s)<3s!(n−s)logn for 1⩽s⩽n−2 and that f(n,s)> [Formula presented] [Formula presented] if s⩾3.

Original languageEnglish
Article number103025
Pages (from-to)1-9
Number of pages9
JournalEuropean Journal of Combinatorics
Volume84
DOIs
Publication statusPublished - 1 Feb 2020

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