6 problems

Let $u_{\mathbb P}(q;n)$ be the quasipolynomial for a piece $\mathbb P$, and write $p_i$ for the period of its coefficient $\gamma_i$. Coefficient-period monotonicity conjecture. T…

For a piece $\mathbb P$ with move set $\mathbf{M}$, write … For a positive integer $\lambda$, let $\mathbb P^{\operatorname{lcm}}_\lambda$ be the lcm-maximal piece whose move set c…

Let $\mathbf{M}$ be the move set of a piece $\mathbb P$, with basic moves $(c_r,d_r)$, and set … Let $\gamma_4$ denote the fourth coefficient of the quasipolynomial…

Let $\mathbf{M}$ be the move set of a piece $\mathbb P$, with basic moves $(c_r,d_r)$, and write … Let $\gamma_3$ denote the third coefficient of the quasipolynomial…

Maximal-move-range piece conjecture. Among all pieces with $\|\mathbb P\|\leq\lambda$, $\mathbb P^{\max}_\lambda$ maximizes the period of every coefficient $\gamma_i$, for fixed…

Let $G$ be an arbitrary graph with $n$ vertices, and consider the configuration $(c,0,0,\dots,0)$, with $c$ chips on one vertex and zero chips on the remaining vertices. Reachable-…