2 problems

Let $k$ be an infinite field and $(R,\mathfrak{m})=k[[x_0,\ldots,x_d]]$. For general linear forms $\ell_1,\ldots,\ell_i\in\mathfrak{m}$, set … Let $\stirlingI{d+1}{d+1-i}$ denote t…

Let $(R,\mathfrak m)$ be a noetherian local ring of dimension $d$ containing a positive characteristic field. Let $J$ be an ideal generated by a full system of parameters, and let…