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On Subsets with Cardinalities of Intersections Divisible by a Fixed Integer
Authors:P Frankl  AM Odlyzko
Institution:1. Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.;2. CNRS, Paris, France;3. Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.
Abstract:If m(n, l) denotes the maximum number of subsets of an n-element set such that the intersection of any two of them has cardinality divisible by l, then a trivial construction shows that
m(n,l)2n/l]
For l= 2, this was known to be essentially best possible. For l ? 3, we show by construction that m(n, l)2?n/l] grows exponentially in n, and we provide upper bounds.
Keywords:
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