6 problems

Let $\mathsf{M}$ be a connected matroid of rank $k$ on $[n]$. Let $\beta(\mathsf{M})$ denote its beta-invariant and let $\operatorname{V}(\mathsf{M})$ denote its volume. Beta-invar…

Planar 4-connectivity conjecture. Then

3-sum conjecture. The invariant satisfies

Let $M$ be a matroid of rank $r$, and write $g_M(t)=\sum_{i\geq 1}g_i(M)t^i$ when the ground set is nonempty. Define the omega invariant by $\omega(M)=g_r(M)$, the coefficient of…

Let $\mathsf{M}$ be a matroid, and let $g_{\mathsf{M}}(t)\in\mathbb{Z}[t]$ denote its $g$-polynomial. Speyer's conjecture. For every matroid $\mathsf{M}$, the polynomial…

Let ${\mathcal G}$ be the invariant of polymatroids defined in the paper, and let $g_{\bf X}(t)$ be Speyer's invariant of a matroid ${\bf X}$. Specialization conjecture. The invari…