5 problems

Let $P$ and $Q$ be posets. Write $P\times Q$ for their Cartesian product, ordered componentwise, and let $\dim(P)$ denote the least integer $n$ such that $P$ is isomorphic to a sub…

Let $P$ be a finite poset, let $|P|$ denote its number of elements, and let $\dim(P)$ denote its order dimension. For a positive integer $m$, let $S_m$ be the standard example on…

Let $P$ be a poset, let $D$ be its order diagram, let $E$ be the edge set of $D$, and let $\phi:E\to\{1,2,\dots,r\}$ be an $r$-coloring of the edges. For a subdiagram $D'$ with ass…

Reversal-ratio conjecture.

A standard example of dimension $m$ is the poset formed by the one-element subsets and the $(m-1)$-element subsets of an $m$-element set, ordered by inclusion. Standard-example con…