Ahlswede–Khachatrian theorem
نویسنده
چکیده
The Erdős–Ko–Rado theorem determines the largest μp-measure of an intersecting family of sets. We consider the analogue of this theorem to t-intersecting families (families in which any two sets have at least t elements in common), following Ahlswede and Khachatrian [1, 2]. We present a proof of the μp version of their theorem, which is adapted from the earlier proofs. Due to the simpler nature of the μp setting, our proof is simpler and cleaner.
منابع مشابه
Ahlswede–Khachatrian Theorems: Weighted, Infinite, and Hamming
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. We extend this theorem to several other settings: the weighted case, the case of infinitely many points, and the Hamming scheme. The weighted Ahlswede–Khachatrian theorem gives the maximal μp measure of a t-inte...
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It is known from a previous paper [3] that Katona’s Intersection Theorem follows from the Complete Intersection Theorem by Ahlswede and Khachatrian via a Comparison Lemma. It also has been proved directly in [3] by the pushing–pulling method of that paper. Here we add a third proof via a new (k,k+1)-shifting technique, whose impact will be exploared elsewhere. The fourth and last of our proofs ...
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