On a problem of Katona on minimal separating systems

Andrew Chi Chih Yao

doi:10.1016/0012-365X(76)90085-6

On a problem of Katona on minimal separating systems

Andrew Chi Chih Yao

电子与信息学部

科研成果: 期刊稿件 › 文章 › 同行评审

8 引用（Scopus）

摘要

Let S be an n-element set. In this paper, we determine the smallest number f(n) for which there exists a family of subsets of S{A₁,A₂,...,A_f(n)} with the following property: Given any two elements x, y ∈ S (x ≠ y), there exist k, l such that A_k ∩ A_l= ∅, and x ∈ A_k, y ∈ A_l. In particular it is shown that f(n)= 3 log₃n when n is a power of 3.

源语言	英语
页（从-至）	193-199
页数	7
期刊	Discrete Mathematics
卷	15
期	2
DOI	https://doi.org/10.1016/0012-365X(76)90085-6
出版状态	已出版 - 1976

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title = "On a problem of Katona on minimal separating systems",

abstract = "Let S be an n-element set. In this paper, we determine the smallest number f(n) for which there exists a family of subsets of S\{A1,A2,...,Af(n)\} with the following property: Given any two elements x, y ∈ S (x ≠ y), there exist k, l such that Ak ∩ Al= ∅, and x ∈ Ak, y ∈ Al. In particular it is shown that f(n)= 3 log3n when n is a power of 3.",

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AB - Let S be an n-element set. In this paper, we determine the smallest number f(n) for which there exists a family of subsets of S{A1,A2,...,Af(n)} with the following property: Given any two elements x, y ∈ S (x ≠ y), there exist k, l such that Ak ∩ Al= ∅, and x ∈ Ak, y ∈ Al. In particular it is shown that f(n)= 3 log3n when n is a power of 3.

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DO - 10.1016/0012-365X(76)90085-6

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ER -

On a problem of Katona on minimal separating systems

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