The Story of Sunflowers

Abstract

Sunflowers, or $\Delta$-systems, are a fundamental concept in combinatorics introduced by Erd\H{o}s and Rado in their paper: {\em Intersection theorems for systems of sets}, J. Lond. Math. Soc. (1) {\bf 35} (1960), 85--90. A sunflower is a collection of sets where all pairs have the same intersection. This paper explores the wide-ranging applications of sunflowers in computer science and combinatorics. We discuss recent progress towards the sunflower conjecture and present a short elementary proof of the best known bounds for the robust sunflower lemma.