5 problems

Let $\operatorname{W}(k,n)$ be the set of maximal collections of pairwise weakly separated $k$-subsets of $[1\dots n]$, and let a $(2,4)$-move replace one of the two indicated memb…

Let $J,J'$ be $k$-element subsets of $[n]$, and let $L(M_J)$ and $L(M_{J'})$ be the corresponding simple $U_q(\widehat{\mathfrak{sl}_k})$-modules. Weak-separation tensor-product co…

Pairwise smallest-minors conjecture. There exists an arrangement of smallest minors $S\subset\binom{[n]}{k}$ containing $I$ and $J$ if and only if either the pair is 1-interlaced,…

For $2\leq k\leq n-2$, let $\widetilde{\Delta}^{Sep}_{k,n}$ be the reduced complex obtained from the weak separation complex of weakly separated $k$-subsets of $[n]$ by removing it…

Let $[m]=\{1,\ldots,m\}$, and let ${\bf m}^{(ws)}_{k \leq l}$ be the compatibility complex whose vertices are the subsets of $[m]$ having at least $k$ and at most $l$ elements, wit…