The weighted complete intersection theorem

Yuval Filmus

doi:10.1016/j.jcta.2017.04.008

The weighted complete intersection theorem

Yuval Filmus

Computer Science

Technion - Israel Institute of Technology

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

Abstract

The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families for t≥2. We extend this theorem to the weighted setting, in which we consider unconstrained families on n points with respect to the measure μ_p given by μ_p(A)=p^|A|(1−p)^n−|A|. Our theorem gives the maximum μ_p measure of a t-intersecting family on n points, and describes all optimal families for t≥2.

Original language	English
Pages (from-to)	84-101
Number of pages	18
Journal	Journal of Combinatorial Theory. Series A
Volume	151
DOIs	https://doi.org/10.1016/j.jcta.2017.04.008
State	Published - 1 Oct 2017

Keywords

Ahlswede–Khachatrian theorem
Erdős–Ko–Rado theorem
Intersecting families
Shifting

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2017.04.008

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abstract = "The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families for t≥2. We extend this theorem to the weighted setting, in which we consider unconstrained families on n points with respect to the measure μp given by μp(A)=p|A|(1−p)n−|A|. Our theorem gives the maximum μp measure of a t-intersecting family on n points, and describes all optimal families for t≥2.",

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AB - The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families for t≥2. We extend this theorem to the weighted setting, in which we consider unconstrained families on n points with respect to the measure μp given by μp(A)=p|A|(1−p)n−|A|. Our theorem gives the maximum μp measure of a t-intersecting family on n points, and describes all optimal families for t≥2.

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KW - Erdős–Ko–Rado theorem

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EP - 101

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

ER -

The weighted complete intersection theorem

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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