The weighted complete intersection theorem

作者：Filmus Yuval^*

来源：Journal of Combinatorial Theory - Series A, 2017, 151: 84-101.

DOI：10.1016/j.jcta.2017.04.008

• Shifting
• Intersecting families
• Erdos-Ko-Rado theorem
• Ahlswede-Khachatrian theorem

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 mu(p), given by mu(p)(A) = p(|A|) (1 - p)(n-|A|). Our theorem gives the maximum pt, measure of a t-intersecting family on n points, and describes all optimal families for t >= 2.

• 出版日期2017-10