3 problems

Let $\mathcal{S}$ be the simplicial affine semigroup under consideration, let $\Bbbk[\mathcal{S}]$ be its semigroup ring, let $E$ be the distinguished generating set, and for…

Explicit Apéry-set conjecture for $\Gamma_6$. The Apéry set of $\Gamma_6$ with respect to $a$ is

Unique-expansion conjecture. The elements of $\operatorname{Ap}(\Gamma_m,a)$ have unique expressions. Hence the tangent cone of $k[[\Gamma_m]]$ is Cohen–Macaulay. This would extend…