More complete intersection theorems

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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. In recent work, we extended this theorem to the weighted setting, giving the maximum μp measure of a t-intersecting family on n points. In this work, we prove two new complete intersection theorems. The first gives the supremum μp measure of a t-intersecting family on infinitely many points, and the second gives the maximum cardinality of a subset of Zm n in which any two elements x,y have t positions i1,…,it such that xij −yij ∈{−(s−1),…,s−1}. In both cases, we determine the extremal families, whenever possible.

Original languageEnglish
Pages (from-to)128-142
Number of pages15
JournalDiscrete Mathematics
Issue number1
StatePublished - Jan 2019


  • Erdos–Ko–Rado theory
  • Extremal combinatorics
  • Intersecting families

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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