4 problems

Let $A$ be a set, and let $r_{\ell}(\mathcal{C}_{n,A})$ and $r_{\ell}(\mathcal{C}_{n,A}^*)$ denote the numbers of regions of level $\ell$ in the arrangements $\mathcal{C}_{n,A}$ an…

Braid-matroid primitive onset conjecture. The onset of representation stability is $n=2i$ for fixed $i eggeq 1$ when $A(n)=cmathrm{OS}(cmathrm{Br}n)$, and is $n=2i$ for fixed…

Braid-matroid onset conjecture. For every $i eggeq 0$, the sequences $cmathrm{OS}(cmathrm{Br}n)^!i$ and $cmathrm{VG}(cmathrm{Br}n)^!i$ start to stabilize exactly when $n=4i$ and…

Classification conjecture. The multi-braid arrangement $(A_\ell,\mathbf{m})$ is free if and only if it is one of the multi-braid arrangements constructed in Corollary. Equivalently…