2 problems

Let $f(n,k,l)$ be the maximum size of an $l$-trace $k$-Sperner family ${\mathcal F}\subseteq 2^{[n]}$. For a family, being $l$-trace $k$-Sperner means that the trace on every $l$-s…

Let $k$ and $l'$ be positive integers with $l'<k$. An $(n-l')$-trace $k$-Sperner family is a family ${\mathcal F}\subseteq 2^{[n]}$ whose trace on every $(n-l')$-set is $k$-Sperner…