MULTILINEAR POLYNOMIALS AND FRANKL-RAY-CHAUDHURI-WILSON TYPE INTERSECTION-THEOREMS

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{lunate} K for each F ε{lunate} F; and |E ∩ F| ε{lunate} L for each pair of distinct sets E, F ε{lunate} F. Then |F| ≤ N(n, s, r). The proof easily generalizes to equicardinal. © 1991.