🔗 Sunflower (Mathematics)

🔗 Mathematics

In the mathematical fields of set theory and extremal combinatorics, a sunflower or ${\displaystyle \Delta }$-system is a collection of sets whose pairwise intersection is constant. This constant intersection is called the kernel of the sunflower.

The main research question arising in relation to sunflowers is: under what conditions does there exist a large sunflower (a sunflower with many sets) in a given collection of sets? The ${\displaystyle \Delta }$-lemma, sunflower lemma, and the Erdős-Rado sunflower conjecture give successively weaker conditions which would imply the existence of a large sunflower in a given collection, with the latter being one of the most famous open problems of extremal combinatorics.