Disjoint systems

Noga Alon; Benny Sudakov

doi:10.1002/rsa.3240060103

Disjoint systems

Noga Alon, Benny Sudakov

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A disjoint system of type (∀, ∃, k, n) is a collection 𝒞 = {𝒜₁,…, 𝒜_m} of pairwise disjoint families of k‐subsets of an n‐element set satisfying the following condition. For every ordered pair 𝒜_i and 𝒜_j of distinct members of 𝒞 and for every A ϵ 𝒜_i there exists a B ϵ 𝒜_j that does not intersect A. Let D_n (∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ⩾ 2,. (Formula Presented.) This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well.

Original language	English (US)
Pages (from-to)	13-20
Number of pages	8
Journal	Random Structures & Algorithms
Volume	6
Issue number	1
DOIs	https://doi.org/10.1002/rsa.3240060103
State	Published - Jan 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
General Mathematics
Computer Graphics and Computer-Aided Design
Applied Mathematics

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10.1002/rsa.3240060103

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title = "Disjoint systems",

abstract = "A disjoint system of type (∀, ∃, k, n) is a collection 𝒞 = \{𝒜1,…, 𝒜m\} of pairwise disjoint families of k‐subsets of an n‐element set satisfying the following condition. For every ordered pair 𝒜i and 𝒜j of distinct members of 𝒞 and for every A ϵ 𝒜i there exists a B ϵ 𝒜j that does not intersect A. Let Dn (∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ⩾ 2,. (Formula Presented.) This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well.",

author = "Noga Alon and Benny Sudakov",

year = "1995",

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doi = "10.1002/rsa.3240060103",

language = "English (US)",

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journal = "Random Structures \& Algorithms",

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publisher = "John Wiley and Sons Ltd",

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AU - Alon, Noga

AU - Sudakov, Benny

PY - 1995/1

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N2 - A disjoint system of type (∀, ∃, k, n) is a collection 𝒞 = {𝒜1,…, 𝒜m} of pairwise disjoint families of k‐subsets of an n‐element set satisfying the following condition. For every ordered pair 𝒜i and 𝒜j of distinct members of 𝒞 and for every A ϵ 𝒜i there exists a B ϵ 𝒜j that does not intersect A. Let Dn (∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ⩾ 2,. (Formula Presented.) This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well.

AB - A disjoint system of type (∀, ∃, k, n) is a collection 𝒞 = {𝒜1,…, 𝒜m} of pairwise disjoint families of k‐subsets of an n‐element set satisfying the following condition. For every ordered pair 𝒜i and 𝒜j of distinct members of 𝒞 and for every A ϵ 𝒜i there exists a B ϵ 𝒜j that does not intersect A. Let Dn (∀, ∃, k) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, k, n). It is shown that for every fixed k ⩾ 2,. (Formula Presented.) This settles a problem of Ahlswede, Cai, and Zhang. Several related problems are considered as well.

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Disjoint systems

Abstract

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