3 problems

Block-partition factorization conjecture. There is an ordering $(\mathbf{T}_1,\ldots,\mathbf{T}_{(d-1)(k-1)-1},\mathbf{S})$ with…

Let $\mathsf{M}$ be a matroid, and let $g_{\mathsf{M}}(t)$ denote its $g$-polynomial. g-polynomial positivity conjecture. The polynomial $g_{\mathsf{M}}(t)$ has positive coefficien…

Let $M$ be a matroid on $[n]$ of rank $d$, and let a matroid subdivision of $M$ be a polyhedral subdivision of its matroid polytope in which every cell is itself a matroid polytope…