5 problems

Effective-bound conjecture. These three quantities equal $2^k-1$ for $k\geq 1$. This conjecture gives the expected sharp value of the embedding dimension bound for the incidence st…

Steiner triple code embedding-dimension conjecture. For every $d\ge 1$ there exists a Steiner triple code $\mathcal{C}$ with

Let ${\mathcal O}=\{1,y,x,y^2,x^2\}$ be the L-shaped order ideal in two indeterminates, and let $\mathbb{B}_{\mathcal O}$ be its border basis scheme. Suppose the scheme is embedded…

Let $S$ be a good subsemigroup of $\mathbb{N}^2$. Its multiplicity vector is denoted by $\boldsymbol{e}$, and let $M=S\setminus\{\boldsymbol{0}\}$. A good semigroup is said to have…

Let $\mathcal{C}$ be an integer cone such that the dimension of the real vector space generated by $\mathcal{C}$ is $p$. A $\mathcal{C}$-semigroup is an affine semigroup whose comp…