4 problems

Let $M_1$ and $M_2$ be matroids on the same ground set, with $M_2$ the dual matroid of $M_1$. A common basis is a basis shared by both matroids, and a reconfiguration sequence is a…

Let $G_1$ and $G_2$ be connected graphs. Their central zonotopal algebras are denoted by $4\mathcal{C}_{G_1}^{\mathcal{C}}4$ and $4\mathcal{C}_{G_2}^{\mathcal{C}}4$. For a graph, i…

Converse conjecture. The algebras ${\mathcal B}_{G_1}^T$ and ${\mathcal B}_{G_2}^T$ are isomorphic if and only if the bridge-free matroids of $G_1$ and $G_2$ are isomorphic.

Independent set conjecture. If $M$ is a triangle-free $3$-connected matroid with a simple $3$-connected minor $N$, then $M$ has an independent set $I$ of $N$-contractible elements…