4 problems

Let $Q$ be a quiver of rank at least $4$, and let $[A_2]$ denote the finite-type $A_2$ quiver. Say that $[A_2]$ embeds into the mutation class of $Q$ when it occurs there under the…

Let $Q$ be a quiver with a reddening sequence, and let the associated permutation of a reddening sequence be the permutation induced by its action on the framing. An embedding of t…

Let $Q$ be a quiver, and let $\operatorname{uRed}(Q)$ denote its unrestricted red size, namely the maximal number of red vertices obtained after an arbitrary mutation sequence. Two…

Let $Q$ be a connected quiver on $n$ vertices that does not admit a reddening sequence. The red size $\operatorname{Red}(Q)$ is the maximal number of red vertices obtained after mu…