On the density of sets of vectors

Noga Alon

doi:10.1016/0012-365X(83)90253-4

On the density of sets of vectors

Noga Alon

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

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Abstract

Answering a question of Erdös, Sauer [4] and independently Perles and Shelah [5] found the maximal cardinality of a collection F of subsets of a set: N of cardinality n such that for every subset M ⊂ N of cardinality m |{C ∩ M: C ε{lunate} F}| < 2^m. Karpovsky and Milman [3] generalised this result. Here we give a short proof of these results and further extensions.

Original language	English (US)
Pages (from-to)	199-202
Number of pages	4
Journal	Discrete Mathematics
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(83)90253-4
State	Published - 1983
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(83)90253-4

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title = "On the density of sets of vectors",

abstract = "Answering a question of Erd{\"o}s, Sauer [4] and independently Perles and Shelah [5] found the maximal cardinality of a collection F of subsets of a set: N of cardinality n such that for every subset M ⊂ N of cardinality m |\{C ∩ M: C ε\{lunate\} F\}| < 2m. Karpovsky and Milman [3] generalised this result. Here we give a short proof of these results and further extensions.",

author = "Noga Alon",

year = "1983",

doi = "10.1016/0012-365X(83)90253-4",

language = "English (US)",

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journal = "Discrete Mathematics",

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publisher = "Elsevier B.V.",

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AB - Answering a question of Erdös, Sauer [4] and independently Perles and Shelah [5] found the maximal cardinality of a collection F of subsets of a set: N of cardinality n such that for every subset M ⊂ N of cardinality m |{C ∩ M: C ε{lunate} F}| < 2m. Karpovsky and Milman [3] generalised this result. Here we give a short proof of these results and further extensions.

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UR - https://www.scopus.com/pages/publications/0001604527#tab=citedBy

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DO - 10.1016/0012-365X(83)90253-4

M3 - Article

AN - SCOPUS:0001604527

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VL - 46

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -

On the density of sets of vectors

Abstract

All Science Journal Classification (ASJC) codes

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