4 problems

The antichain trace conjecture. Let $k$ be a non-negative integer and let $n\geq 2k$. If $\mathcal{F}\subset 2^{[n]}$ is an antichain satisfying…

The general arrow-relation conjecture. For all integers $n>\ell>0$,

Let $B$ be the butterfly poset on four elements $a,b,c,d$, with $a,b<_B c,d$. For a family $\mathcal F\subseteq 2^{[n]}$, let $Tr_{n-1}(n,B)$ denote the maximum size of a family wh…

Let $P$ be a poset, let $e(P)$ be the largest integer $k$ such that, for every $j$ and $n$, the family … is $P$-free, and let $Tr_{n-k}(n,P)$ denote the maximum size of a family wh…