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Revision #2 to TR22-005 | 13th May 2022 21:08

Sunflowers: from soil to oil

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Revision #2
Authors: Anup Rao
Accepted on: 13th May 2022 21:08
Downloads: 0
Keywords: 


Abstract:

A \emph{sunflower} is a collection of sets whose pairwise intersections are identical. In this article, we shall go sunflower-picking. We find sunflowers in several seemingly unrelated fields, before turning to discuss recent progress on the famous sunflower conjecture of Erd\H{o}s and Rado, made by Alweiss, Lovett, Wu and Zhang.



Changes to previous version:

The current version uses better notation that simplifies some equations.


Revision #1 to TR22-005 | 12th May 2022 20:03

Sunflowers: from soil to oil





Revision #1
Authors: Anup Rao
Accepted on: 12th May 2022 20:03
Downloads: 0
Keywords: 


Abstract:

A \emph{sunflower} is a collection of sets whose pairwise intersections are identical. In this article, we shall go sunflower-picking. We find sunflowers in several seemingly unrelated fields, before turning to discuss recent progress on the famous sunflower conjecture of Erd\H{o}s and Rado, made by Alweiss, Lovett, Wu and Zhang, as well as a related resolution of the \emph{threshold vs expectation threshold conjecture} of Kahn and Kalai discovered by Park and Pham. We give short proofs for both of these results.



Changes to previous version:

The resolution of the conjecture of Kahn and Kalai is now discussed. A short and self-contained proof of both the conjecture and the sunflower bound is added.


Paper:

TR22-005 | 11th January 2022 21:30

Sunflowers: from soil to oil





TR22-005
Authors: Anup Rao
Publication: 11th January 2022 21:30
Downloads: 566
Keywords: 


Abstract:

A \emph{sunflower} is a collection of sets whose pairwise intersections are identical. In this article, we shall go sunflower-picking. We find sunflowers in several seemingly unrelated fields, before turning to discuss recent progress on the famous sunflower conjecture of Erd\H{o}s and Rado, made by Alweiss, Lovett, Wu and Zhang.



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