On Subsets with Cardinalities of Intersections Divisible by a Fixed Integer |
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Authors: | P Frankl AM Odlyzko |
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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. |
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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 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. |
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