6 problems

Let $A$ be an integer matrix, let $I_A$ be its toric ideal, and define the $A$-degree of a binomial $x^u-x^v$ with $\deg_A(x^u)=\deg_A(x^v)$ by $\deg_A(x^u-x^v)=\deg_A(x^u)$. A pri…

Let $I_A$ be a toric ideal, and let the true degree of a circuit of $A$ mean the degree computed without dividing by the common factor $c$ in the circuit formula. Sturmfels's conje…

Graver-basis conjecture. Every robust toric ideal is minimally generated by its Graver basis ${\mathcal Gr}(A)$. Consequently, robust toric ideals would be precisely the…

Let $W a a$ be a rational linear subspace. For $z a a a Wcapmathbb{Z}^n$, a conformal circuit decomposition is a representation of $z$ as a sum of conformal circuit vectors. A vect…

Let $K_{3,m}$ be the complete bipartite graph with parts of sizes $3$ and $m$, and let its Graver complexity denote the maximum type of an element in the Graver basis associated wi…

The true circuit conjecture. For every $B\in Gr_A$,