论文信息 - Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems

Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems

Abstract We give a very simple new proof of the celebrated intersection theorem of D. K. Ray-Chaudhuri and R. M. Wilson. The new proof yields a generalization to nonuniform set systems. Let N(n,s,r) = ( n s ) + ( n s−1 ) + ⋯( n s−r+1 ). Generalized Ray-Chaudhuri-Wilson Theorem. Let K = {k1,…,kr}, L = {l1,…,ls}, and assume ki > s − r for all i. Let F be a family of subsets of an n-element set. Suppose that |F| ϵ K for each F ϵ F ; and |E ∩ F| ϵ L for each pair of distinct sets E, F ϵ F . Then | F | ⩽ N(n, s, r). The proof easily generalizes to equicardinal

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