6 problems

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 $M$ be a matroid, and let $g_M(t)\in\mathbb{Z}[t]$ be the covaluative matroid invariant described in the paper. Nonnegativity conjecture for $g_M(t)$. For any matroid $M$, the…

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…