In mathematical Set Theory, a collection of distinct sets is called a Sunflower (a.k.a. a Ξ-system) if the intersection of any pair of sets equals the common intersection of all the sets.
In the 1960s, mathematicians ErdΕs and Rado (and others) investigated the minimum number of sets of size r needed to guarantee the existence of a sunflower of a given size. - but could not formulate an answer.
The problem remains open, despite the fact that Sunflowers are fundamental objects in external set theory, and have relations and applications to many other areas of mathematics and theoretical computer science.
A 2021 paper published in arXiv, noted :
Despite a lot of recent attention including a polymath project and some amazing breakthroughs, even the asymptotic answer remains unknown.β
Source : arXiv:2110.11319 (math)
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