More complete intersection theorems

摘要

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 mu(p) measure of a t-intersecting family on n points. In this work, we prove two new complete intersection theorems. The first gives the supremum mu(p) measure of a t-intersecting family on infinitely many points, and the second gives the maximum cardinality of a subset of Z(m)(n) in which any two elements x, y have t positions i(l), ... , i(t) such that x(ij) - y(ij) is an element of {-(s - 1), ... , s - 1}. In both cases, we determine the extremal families, whenever possible. (C) 2018 Elsevier B.V. All rights reserved.