2 problems

Let $v,w\in S_n$, let $I_{v,w}$ be the associated Kazhdan–Lusztig ideal, and let $\prec_{v,w,\pi}$ be one of the term orders determined by a generalized antidiagonal permutation…

Let $v,w$ be permutations with $v\leq w$, and let $I_{v,w}$ denote the Kazhdan–Lusztig ideal. Suppose that $I_{v,w}$ is standardly homogeneous. If $ws_i<w$ but $vs_i>v$, then…