6 problems

Let $\Delta$ be a complete fan of dimension $n$, and let ${\mathcal A}(B\Delta)$ be its associated graded algebra with elements $L_i\in {\mathcal A}(B\Delta)$ of degree $e_i$, for…

Let $L$ be a lattice and let $\sigma$ and $\sigma'$ be cones in a fan, represented by generators $\sigma\leftrightarrow\{v_1,\ldots,v_k\}$ and…

Filtration monotonicity under refinement. One has

Baskoro–et al.'s conjecture. The upper bound

Let $V=(\mathbf{v}_1,\ldots,\mathbf{v}_m)$ be an $n\times m$ F-matrix. Let $\mathcal{M}$ be the set of minimal $n$-dimensional simplicial cones generated by columns of $V$. A pseud…

For each vertex $v$ of the exchange graph, let $\operatorname{Cone}(v)$ be the cone in $V^*$ spanned by the weights $\mathbf g(x^v_e)$ for $e\in I(v)$. A fan is a collection of con…