5 problems

Let $\tau$ be an arbor and let $\mathcal Q_\tau$ be its associated arbor polytope. Let ${\rm Ehr}(\mathcal Q_\tau,t)$ denote its Ehrhart polynomial, and let…

Let $\tau$ be an arbor on the ground set $[n]:=\{1,2,\dots,n\}$, and let $\mathcal Q_\tau$ be its associated $n$-dimensional arbor polytope. Define…

Let $\sigma$ be an arbor, and let $\mathcal Q_\sigma$ be its arbor polytope. Cha's real-rootedness conjecture. All roots of the Ehrhart polynomial of $\mathcal Q_\sigma$ are real a…

Let $E$ be an $n$-element set and let $\tau$ be an arbor on $E$. Its $h$-polynomial is $h(\tau,t)=\sum_{i=0}^n h_i(\tau)t^i$, where $h_i(\tau)$ counts the lattice points of the arb…

Let $\tau$ be an arbor of size $n$, let $\mathcal Q_\tau$ be its associated arbor polytope, and let $\mathcal D(v)$ denote the union of the blocks at the descendants of a vertex…