The paper proves the optimal Daykin-Erdős bound on disjoint pairs, the Singer-Sudan conjecture, and optimal log-rank-style rectangle bounds for sparse and integer-valued matrices.
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Disjoint pairs in set systems and combinatorics of low rank matrices
The paper proves the optimal Daykin-Erdős bound on disjoint pairs, the Singer-Sudan conjecture, and optimal log-rank-style rectangle bounds for sparse and integer-valued matrices.