A Note on k-Wise Oddtown Problems

被引：2
|
作者：
O'Neill, Jason [1 ]
Verstraete, Jacques [1 ]
机构：
[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
来源：
GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 03期
基金：
美国国家科学基金会;
关键词：
Set systems; Covering hypergraphs; Kneser graphs; Intersecting set pairs; SUBSETS;
D O I：
10.1007/s00373-022-02504-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For integers 2 <= t <= k, we consider a collection of k set families Aj:1 <= j <= k where Aj={Aj,i subset of[n]:1 <= i <= m}and |A1,i1 boolean AND only if at least t of the i(j) are distinct. In this paper, we prove that m = O-(n1/[k/2]) when t = k and m = O(n(1)/(t-1)when 2t = 2 <= k and prove that both of these bounds are best possible. Specializing to the case where A = A(1) = ... = A(k), we recover a variation of the classical oddtown problem.
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页数：12
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