2 problems

Let $G$ and $H$ be graphs on $n$ and $m$ vertices, respectively, with $n,m\geq 3$. Let $J_{G,H}$ be the associated binomial edge ideal, let $\ell(J_{G,H})$ denote its analytic spre…

Let $(n,r,b)$ be integers with $0<r\leq n$ and $1\leq b\leq\binom{n}{r}$. A linear $(n,r,b)$-matroid is a matroid with $n$ elements, rank $r$, and exactly $b$ bases that is represe…