On Subsets with Intersections of Even Cardinality

E.R. Berlekamp

doi:10.4153/CMB-1969-059-3

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This paper solves a question posed by P. Erdös:

If A1, A2, …, A are distinct subsets of n elements and if |Ai ∩ Ai| ≡ 0 mod 2 (i ≠ j), then

and for each n, there exists a collection of subsets which achieves this bound with equality.

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