A short proof of the nonuniform Ray-Chaudhuri-Wilson inequality

Abstract

LetL be a set ofs nonnegative integers and ℱ a family of subsets of ann-element setX. Suppose that for any two distinct membersA,B∈ℱ we have¦A ∩ B¦∈ L. Assuming in addition that, ℱ is uniform, i.e. each member of ℱ has the same cardinality, a celebrated theorem of D. K. Ray-Chaudhuri and R. M. Wilson asserts that ¦ℱ¦≦

P. Frankl and R. M. Wilson proved that without the uniformity assumption, we have

.

We give a short proof of this latter result.

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Babai, L. A short proof of the nonuniform Ray-Chaudhuri-Wilson inequality. Combinatorica 8, 133–135 (1988). https://doi.org/10.1007/BF02122561

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  • 05 C 65