Maximum hitting for n sufficiently large

Ben Barber

doi:10.1007/s00373-012-1281-9

Maximum hitting for n sufficiently large

Ben Barber

Pure Mathematics

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

Abstract

For a left-compressed intersecting family A ⊆[n](r) and a set X ⊆ [n], let (Formula Presented). Borg asked: for which X is {pipe}A(X){pipe} maximised by taking A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r. © 2013 Springer Japan.

Original language	English
Pages (from-to)	267-274
Number of pages	8
Journal	Graphs and Combinatorics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s00373-012-1281-9
Publication status	Published - Mar 2014

Keywords

Compression
Erdo{double acute}s-Ko-Rado theorem
Generating set
Intersecting family

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10.1007/s00373-012-1281-9

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title = "Maximum hitting for n sufficiently large",

abstract = "For a left-compressed intersecting family A ⊆[n](r) and a set X ⊆ [n], let (Formula Presented). Borg asked: for which X is {pipe}A(X){pipe} maximised by taking A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r. {\textcopyright} 2013 Springer Japan.",

keywords = "Compression, Erdo{double acute}s-Ko-Rado theorem, Generating set, Intersecting family",

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AB - For a left-compressed intersecting family A ⊆[n](r) and a set X ⊆ [n], let (Formula Presented). Borg asked: for which X is {pipe}A(X){pipe} maximised by taking A to be all r-sets containing the element 1? We determine exactly which X have this property, for n sufficiently large depending on r. © 2013 Springer Japan.

KW - Compression

KW - Erdo{double acute}s-Ko-Rado theorem

KW - Generating set

KW - Intersecting family

UR - http://www.mendeley.com/catalogue/maximum-hitting-n-sufficiently-large

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DO - 10.1007/s00373-012-1281-9

M3 - Article

SN - 0911-0119

VL - 30

SP - 267

EP - 274

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 2

ER -

Maximum hitting for n sufficiently large

Abstract

Keywords

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