5 problems

Motion conjecture under bounded constituent degrees. If every constituent has degree at most $\delta n$, then

Motion conjecture for primitive coherent configurations. If $\mathfrak X$ is not a Cameron scheme, then there is a positive constant $c$ such that

Fix $0<\delta<1$. Let $\mathfrak{X}$ be a primitive coherent configuration on $n$ vertices, and suppose every constituent has degree at most $\delta n$. Sublinear-rank motion conje…

Let $\mathfrak{X}$ be a primitive coherent configuration on $n$ vertices. For a group $G$, its thickness $\theta(G)$ is the greatest $t$ such that the alternating group $A_t$ is in…

Commutative coherent configuration conjecture. There exist commutative coherent configurations ${\cal C}_n$ realizing $\langle n,n,n\rangle$ and of rank $n^{2+o(1)}$.