Lower bounds for the Turán densities of daisies

David Ellis, Dylan King

For integers $r\ge 3$ and $t\ge 2$, an $r$-uniform $t$-daisy ${\mathcal{D}}_r^t$ is a family of $\left(\genfrac{}{}{0ex}{}{2t}{t}\right)$ $r$-element sets of the form $$\{S \cup T \ : T\subset U, \ |T|=t…