Multilinear polynomials and a conjecture of Frankl and Füredi
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.
scientific article; zbMATH DE number 1278834