5 problems

For each positive integer $n$, let $\mathsf{S}_n$ be the sparse paving matroid on $[n]$ of rank $\lfloor n/2\rfloor$ with the maximal possible number of circuit-hyperplanes and lex…

Let $\mathcal{G}$ be a proper minor-closed graph class, and let $G$ be a connected $n$-vertex graph in $\mathcal{G}$. The spanning tree polytope of $G$ is the convex hull of the in…

Let $\mathcal{C}$ be a proper minor-closed family of graphs, and let $G=(V,E)$ be a connected graph in $\mathcal{C}$. Let $\operatorname{P_{\mathrm{sp.trees}}}(G)$ denote the conve…

Generic maximal-rank conjecture. The combinatorial hypersimplices of nonnegative rank $2n$ form a dense open subset of $\mathcal{R}_{n,k}$.

Let $S_n$ be the slack matrix of any $n$-gon, and let $\lfloor x\rfloor$ denote the largest integer not exceeding $x$. Polygon slack-matrix upper-bound conjecture. … and equality h…