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Multilinear Polynomials and a Conjecture of Frankl and Furedi

机译:多元线性多项式与Frankl和Furedi的猜想

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Frankl and Furedi conjectured that given a family J of subsets of [n] such that 1 <= |E intersect F| <= k for all distinct E and f in J. we must have |J| <= #SIGMA#_(i=0)~k (_i~(n - 1)), (1981, P. Frankl and Z. Furedi, Collog. Math. Soc. Janos Bolyai 37, 305 320). The first proof of this result was given by G. V. Ramanan in (1997, J. Combin. Ser. A 79, 53 67). In this note, we present a proof which is a modification of an approach to this problem by H. Snevily (1994, J. Combin. Ser. A. 68, 232 238) and like Snevily's, is based on the technique of N. Alon, L. Babai, and H. Suzuki (1991, J. Combin, Theory Ser. A 58, 165 180).
机译:弗兰克(Frankl)和弗雷迪(Furedi)猜想给定一个[n]子集的族J,使得1 <= | E与F |相交。 <= k对于J中所有不同的E和f。我们必须具有| J |。 <= #SIGMA #_(i = 0)〜k(_i〜(n-1)),(1981,P.Frankl和Z.Furedi,Collog.Math.Soc.Janos Bolyai 37,305320)。该结果的第一个证据由G. V. Ramanan在(1997,J. Combin。Ser。A 79,53 67)中给出。在本注释中,我们提供了一个证明,它是对H. Snevily(1994,J. Combin。Ser。A. 68,232 238)的一种解决方法的修改,并且与Snevily一样,也是基于N的技术。 Alon,L。Babai和H.Suzuki(1991,J.Combin,Theory Ser.A 58,165180)。

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