4 problems

Top-socle Lex Plus Powers conjecture. Then

Let $R=K[x_1,\ldots,x_n]$, and let $I$ be a homogeneous ideal containing a regular sequence of degrees $2\leq a_1\leq\ldots\leq a_n$. Let $L$ be a lex-plus-powers ideal associated…

Let $cmathfrak{m}$ be a multisegment, and let $cLambda(cmathfrak{m})$ be its RSK-standard representation. Let $Z(cmathfrak{m})$ denote the irreducible representation attached to…

Let $\Delta$ be a connected orientable homology $(d-1)$-manifold without boundary whose vertex links have the weak Lefschetz property. Let $\Theta$ and $w$ be as in Theorem 5.4, se…