5 problems

Let ${\mathcal{A}}$ be a rank $r$ central multiarrangement in $\mathbb{C}^n$ with $|{\mathcal{A}}|=m$. Define … Here $\Omega_n$ is the superspace algebra, $\lambda_L$ is the linear…

Logarithmic-concavity conjecture. The Hilbert sequence of $\mathscr{C}_G^f$ is logarithmically concave for all graphs $G$ and all non-degenerate functions $f$.

Let $\mathcal{A}$ be a central hyperplane arrangement with associated matroid $M_{\mathcal{A}^!}$ on ground set $E$, let $L$ be the relevant vector space, and write…

Let $A_1\in\mathbb{R}^{n_1\times m_1}$ and $A_2\in\mathbb{R}^{n_2\times m_2}$ have ranks $n_1$ and $n_2$, respectively. A column is a bridge-column if deleting it decreases the ran…

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…