Improved bounds for the sunflower lemma

@article{Alweiss2019ImprovedBF,
  title={Improved bounds for the sunflower lemma},
  author={Ryan Alweiss and Shachar Lovett and Kewen Wu and Jiapeng Zhang},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  year={2019}
}
  • Ryan Alweiss, Shachar Lovett, +1 author Jiapeng Zhang
  • Published 2019
  • Mathematics, Computer Science
  • Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
  • A sunflower with r petals is a collection of r sets so that the intersection of each pair is equal to the intersection of all. Erdős and Rado proved the sunflower lemma: for any fixed r, any family of sets of size w, with at least about ww sets, must contain a sunflower. The famous sunflower conjecture is that the bound on the number of sets can be improved to cw for some constant c. In this paper, we improve the bound to about (logw)w. In fact, we prove the result for a robust notion of… CONTINUE READING
    19 Citations
    Note on Sunflowers
    Near-sunflowers and focal families
    Coding for Sunflowers
    • A. Rao
    • Computer Science, Mathematics
    • ArXiv
    • 2019
    • 8
    • PDF
    Monotone Circuit Lower Bounds from Robust Sunflowers
    • 1
    • Highly Influenced
    • PDF
    On the size of shadow-added intersecting families
    On the size of maximal intersecting families
    The Karger-Stein algorithm is optimal for k-cut
    • 3
    • PDF
    Negligible obstructions and Tur\'an exponents
    • 2
    • PDF
    Rainbow independent sets in certain classes of graphs.
    • 3
    • PDF

    References

    SHOWING 1-4 OF 4 REFERENCES
    Intersection Theorems for Systems of Sets
    • 171
    • Highly Influential
    The Monotone Complexity of k-clique on Random Graphs
    • 30
    • Highly Influential
    The Monotone Complexity of k-clique on Random Graphs
    • B. Rossman
    • Mathematics, Computer Science
    • 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
    • 2010
    • 36
    • Highly Influential
    • PDF
    The Permanent Rank of a Matrix
    • Yang Yu
    • Mathematics, Computer Science
    • J. Comb. Theory, Ser. A
    • 1999
    • 20
    • Highly Influential