Sunflower problems in 3-uniform intersecting hypergraphs

In order to get better understand and study the famous Erdős’s sunflower conjecture, Frankl and Wang introduces the function 𝑚 𝑘 ⁡ ( 𝑟 0 , 𝑟 1 , … , 𝑟 𝑘 − 1 ) , which represents the maximum size of a collection of distinct k -sets such that, for every i from 0 to 𝑘 − 1 , the largest sunflower within the collection with a center of size i has a size that is no greater than r i . They obtained the exact value of m 3 (1, r, r ), which can be regarded as the sunflower problem in 3-uniform intersecting hypergraphs. It is nature to consider the general problem for m 3 (1, r, s ). In this paper, we obtain the exact value of m 3 (1, r, s ), which solves this problem in 3-uniform intersecting hypergraphs.