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수리 및 계산 과학 연구단
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Covering radius in the Hamming permutation space

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Title
Covering radius in the Hamming permutation space
Author(s)
Hendrey K.; Wanless I.M.
Publication Date
2020-02
Journal
EUROPEAN JOURNAL OF COMBINATORICS, v.84, no., pp.103025 -
Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Abstract
© 2019 Elsevier LtdLet 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! [Formula presented] [Formula presented] if s⩾3
URI
https://pr.ibs.re.kr/handle/8788114/6394
ISSN
0195-6698
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > Journal Papers (저널논문)
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