2 problems

Let $M$ be a matroid and let $I_{\Delta(M)}$ be its Stanley–Reisner ideal. Write $\widehat{\rho}(I_{\Delta(M)})$ for its asymptotic resurgence, $\omega(I_{\Delta(M)})$ for the larg…

Let $R$ be the polynomial ring in $n$ variables, and let $\mathbf{c}=(c_p,\dots,c_0)$ be a strictly decreasing sequence of integers with $p\leq n$. A pure Betti diagram has shift t…