3 problems

Let $M$ be a connected matroid, and let $P_M$ be its base polytope. Say that $P_M$ admits a series-parallel subdivision if it can be subdivided into base polytopes of series-parall…

Connected series-parallel subdivision conjecture. The polynomial $\wwtilde{g}_{\mathsf{M}}(t-1)$ has non-negative coefficients. This is a stronger positivity statement beyond Schub…

Let $\mathcal{S}$ be a subdivision of $\Delta_{k,n}$ into smaller matroid polytopes. For each $1\leq i\leq n$, let $f_i$ be the number of cells of $\mathcal{S}$ of dimension $n-i$…