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Near-sunflowers and focal families

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Abstract

We present some problems and results about variants of sunflowers in families of sets. In particular, we improve an upper bound of the first author, Körner and Monti on the maximum number of binary vectors of length n so that every four of them are split into two pairs by some coordinate. We also propose a weaker version of the Erdős–Rado sunflower conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Noga Alon

  2. Schools of Mathematics and Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Noga Alon

  3. Department of Mathematics, Technion—Israel Institute of Technology, Technion City, Haifa, 3200003, Israel

    Ron Holzman

Authors
  1. Noga Alon
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  2. Ron Holzman
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Correspondence to Ron Holzman.

Additional information

Dedicated to Nati Linial, on his 70th birthday

Research supported in part by NSF grant DMS-2154082 and BSF grant 2018267.

Research performed during a visit at the Department of Mathematics, Princeton University, supported by the H2020-MSCA-RISE project CoSP–GA No. 823748.

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Alon, N., Holzman, R. Near-sunflowers and focal families. Isr. J. Math. 256, 21–33 (2023). https://doi.org/10.1007/s11856-023-2500-1

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  • DOI: https://doi.org/10.1007/s11856-023-2500-1

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