5 problems

Let $\mathcal{F}$ be a family and let $\mathcal{S}_{\mathcal{F},k}^*$ be its partial signed-set family. A family has the strict $t$-star property if every largest $t$-intersecting…

Let $t\geq1$ and let $\mathcal{F}$ be any family. For each $k$, let $\mathcal{S}_{\mathcal{F},k}$ be the associated signed-set family, and say it has the strict $t$-star property w…

Let $t\geq1$ and let $\mathcal{F}$ be any family. For each $k$, let $\mathcal{S}_{\mathcal{F},k}$ be the associated signed-set family, and let $k_0(t)$ be the least threshold for t…

Let $\mathcal{F}$ be a family, let $k\geq2$, and let $\mathcal{S}_{\mathcal{F},k}$ be its signed-set family. A family has the $t$-star property if a largest $t$-intersecting subfam…

Let $\mathcal{F}$ be a family and let $k\geq2$. The signed-set family $\mathcal{S}_{\mathcal{F},k}$ consists of sets obtained by assigning one of $k$ labels to each element of a me…