7 problems

Let $P$ be a finite poset. A local realizer of $P$ is a family of partial linear extensions whose frequency is the maximum number of partial linear extensions in which any element…

Multiplicative lower-bound conjecture. Among cover-planar posets,

Dimension-boundedness conjecture. The class of cover-planar posets is $\dim$-bounded.

Let $H$ be a graph. Call $H$ unavoidable if the cover graph of every poset of sufficiently large dimension contains $H$ as a minor. Kelly's construction refers to the family of pla…

Let $H_d\simeq \mathbb{R}^{d-1}$ be the hyperplane used for the $d$-dimensional construction, let $R$ be a $d$-representation, and let $\Sigma(R)$ be the abstract simplicial comple…

Let $\mathcal{C}$ be a monotone class of graphs. For each fixed $h\geq 1$, consider posets of height at most $h$ whose cover graphs belong to $\mathcal{C}$. Bounded-expansion chara…

Bounded-expansion characterization. The class $\mathcal{C}$ has bounded expansion if and only if, for each $h\geq 1$, the posets of height $h$ whose cover graphs are in…