Bounds on Pairs of Families with Restricted Intersections

such that for any , . We are interested in the maximum product , given r and L. We give asymptotically optimal bounds for L containing only elements of s<q residue classes modulo q, where q is arbitrary (even non-prime) and s is a constant. As a consequence, we obtain a version of the Frankl–Rödl result about forbidden intersections for the case of two forbidden intersections. We also give tight bounds for L={0,...,k}.

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Received: August 5, 1998

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Sgall, J. Bounds on Pairs of Families with Restricted Intersections. Combinatorica 19, 555–566 (1999).

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  • AMS Subject Classification (1991) Classes:  05D05; 68R05