3 problems

Let a wedge of cycles be a graph obtained by gluing cycles at vertices, and equip it with an asymmetric initial configuration. Wedge-cycle variety conjecture. Wedges of more than t…

Let $C_n$ be the directed cycle on $n$ vertices with no sinks. Let $\mathbf{c}_0$ be a binary configuration with $|\mathbf{c}_0|>1$, and let $1\leq k\leq n$. For $1\leq i\leq n$, d…

Let $P_n$ be the directed path on $n$ vertices, let $\beta_i$ denote the $i$-th Betti number of its avalanche complex, and let a binary configuration be an initial configuration wh…