Set systems with \(\mathcal L\)-intersections modulo a prime number
type: Item
instance of: scholarly article
title: Set systems with \(\mathcal L\)-intersections modulo a prime number
zbMATH Open document ID: 1175.05005
author: William Y. C. Chen
author: Jiuqiang Liu
published in: Journal of Combinatorial Theory. Series A
publication date: 2009-03-04T00:00:00Z
review text: Let \(p\) be a prime, \(L= \{l_1,l_2,\dots, l_s\}\) and \(K= \{k_1,k_2,\dots, k_r\}\) be two disjoint subsets of \(\{0,1,2,\dots, p-1\}\). Suppose \(F= \{F_1,F_2,\dots, F_m\}\) is a family of subsets of \(\{1,2,\dots, n\}\) such that \(|F_i\cap F_j|\pmod p\in L\) for every pair \(i\neq j\) and \(|F_i|\pmod p\in K\) for every \(1\leq i\leq m\). In [Combinatorica 23, No. 3, 527--533 (2003; Zbl 1045.05087)] \textit{H. S. Snevily} conjectured that \(|F|\leq{n\choose s}\). In this paper the authors show that if \(F\) is a \(k\)-uniform family of subsets of \(\{1,2,\dots, n\}\), then the above-mentioned conjecture is true.
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 5523120
zbMATH Keywords: set system
zbMATH Keywords: prime modulo
zbMATH Keywords: Erdős-Ko-Rado theorem
zbMATH Keywords: Frankl-Ray-Chaudhuri-Wilson theorems
zbMATH Keywords: Frankl-Füredi's conjecture
zbMATH Keywords: Snevvily's conjecture
reviewed by: Le Maohua
MaRDI profile type: Publication
full work available at URL: j.jcta.2008.04.008
OpenAlex ID: W1995895515
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DOI: 10.1016/J.JCTA.2008.04.008
description: scientific article; zbMATH DE number 5523120