We show that a family $\mathcal{ F}$ of sets each of cardinality $m \in \mathbb{ Z}_{ >2}$ includes a $k$-sunflower if $ |\mathcal{ F}| \ge \left( \frac{ c k^2 \ln m}{ \ln \ln m} \right)^m$ for some constant $c>0$, where $k$-sunflower means a family of $k$ different sets with a common pairwise intersection. The base of the exponential lower bound is sub-logarithmic for each $k$ updating the current best-known result.
Categories: math.CO
