3 problems

Let $n>3$ and let $q otin Z(\operatorname{Quat}{n+1})$. Consider the space ${cal L}n(1;q)$ of locally convex curves with endpoint data $(1,q)$. If it contains convex curves, let…

Let $S_{n+1}$ be the symmetric group, let ${\mathbf W}_n$ be the set of words, and let $\operatorname{inv}(\sigma)$ denote the inversion number of $\sigma$. For a nonidentity permu…

Let $S_{n+1}$ be the symmetric group, let ${\mathbf W}_n$ be the set of words in the relevant alphabet, and let $\operatorname{mult}:S_{n+1}\to\mathbb{N}^n$ be given by … Extend th…