Multilinear polynomials and a conjecture of Frankl and Füredi
type: Item
instance of: scholarly article
title: Multilinear polynomials and a conjecture of Frankl and Füredi
zbMATH Open document ID: 0916.05070
author: Arvind Sankar
author: Sundar Vishwanathan
published in: Journal of Combinatorial Theory. Series A
publication date: 1999-07-07T00:00:00Z
review text: Let \(S\) be a set of integers. A set system \(\mathcal F\) on \(\{ 1,\ldots, n\}=[n]\) is \(S\)-intersecting, if the cardinality of every pairwise intersection belongs to \(S.\) The Frankl-Füredi conjecture, which is closely related to the non-uniform Ray-Chaudhary-Wilson theorem of Frankl and Wilson, can be formulized as follows: Let a family \(\mathcal F\) on \([n]\) satisfy that every pairwise intersection has at least 1 but at most \(k\) elements. Then \[ | {\mathcal F}| \leq \sum_{i=0}^k {n-1\choose i}. \] This statement was proved first by \textit{G. V. Ramanan} [J. Comb. Theory, Ser. A 79, No. 1, 53-67, Art. No. TA962774 (1997; Zbl 0882.05120)]. This paper gives a new, simpler proof for the conjecture, using H. S. Snevily's approach.
Mathematics Subject Classification ID: 05D05
zbMATH DE Number: 1278834
zbMATH Keywords: multilinear polynomial
zbMATH Keywords: Ray-Chaudhury-Wilson theorem
zbMATH Keywords: Frankl-Wilson theorem
zbMATH Keywords: set system
zbMATH Keywords: intersection
zbMATH Keywords: Frankl-Füredi conjecture
reviewed by: Péter L. Erdős
Wikidata QID: Q123021944
MaRDI profile type: Publication
OpenAlex ID: W1967747021
cites work: Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems
cites work: A short proof of the nonuniform Ray-Chaudhuri-Wilson inequality
cites work: Q3693528
cites work: Intersection theorems with geometric consequences
cites work: On t-designs
cites work: Proof of a conjecture of Frankl and Füredi
cites work: On generalizations of the deBruijn-Erdős theorem
DOI: 10.1006/JCTA.1998.2914
description: scientific article; zbMATH DE number 1278834