Disjoint systems

Noga Alon, Benny Sudakov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 ∈ Ai there exists a B ∈ 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.

Original languageEnglish
Title of host publicationAlgebraic Coding - 1st French-Israeli Workshop, Proceedings
EditorsGerard Cohen, Antoine Lobstein, Gilles Zemor, Simon Litsyn
PublisherSpringer Verlag
Number of pages5
ISBN (Print)9783540578437
StatePublished - 1994
Event1st French-Israeli Workshop on Algebraic Coding, 1993 - Paris, France
Duration: 19 Jul 199321 Jul 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume781 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference1st French-Israeli Workshop on Algebraic Coding, 1993


FundersFunder number
BSF Grant
United States - Israel BSF
United States - Israel Binational Agricultural Research and Development Fund


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