7 problems

Let $w\in \mathfrak{S}_n$ be a $321$-avoiding and $2$-repeating permutation. Let $u,v\in\mathfrak{S}_n$ satisfy $u\leq v\leq w$, and let $\tilde{R}_{u,v}(t)$ denote the correspondi…

Contractible-complex conjecture. There is a contractible complex whose fundamental $n$-cells are given by diagrams with $2n+6$ endpoints, each one connected to the same odd number…

Relations-between-relations conjecture. The $2$-complex $C$ has precisely these types of $2$-cells.

Skew-shape generalization. Theorem MainStraight holds more generally when $[bc^*]$ and $[bb^*]$ are $e$-small skew shapes rather than straight shapes.

Let $F$-, $\Delta$-, and $\Delta^2$-symbols implement basis transformations for diagrams involving fusion, shrinking, and hierarchical shrinking processes. The paper verifies that…

Six-cycle spanning conjecture. For $m,n\in\mathbb{N}$, these component-planar graphs span

Faithfulness conjecture. The functor $\operatorname{Kar}(\Phi)$ is faithful, and hence is an equivalence of categories.