8 problems

Kellerhals–Perren's conjecture. These growth rates should be Perron numbers.

Perron-number conjecture. The growth rate of any Coxeter system of dimension at most $2$ is a Perron number.

Parry-power conjecture. For every $d\geq6$, $4\theta_d4$ is Parry, and for every integer $k\geq2$, $4\theta_d^k4$ is non-Parry.

Non-Parry powers conjecture. For every $d\geq4$ and every integer $k\geq1$, the power $4\beta_d^k4$ is non-Parry.

Density conjecture. The set $4\mathcal{H}_14$ is dense in $(1,\infty)$.

Dynamical strong Lehmer conjecture. If $4\beta<\tau_{10}4$ is a Perron number, then $4\beta^n4$ is a Parry number for only finitely many integers $4n4$.

Weak-Perron dynamical-degree question. Is every dynamical degree of an element of $\operatorname{End}(\mathbb{A}^n_{\mathbf{k}})$ a weak Perron number of degree at most $n$, respec…

Lind's conjecture. The smallest Perron number of degree $n\geqslant 2$ should have minimal polynomial $x^n-x-1$. This conjecture identifies a proposed extremal Perron number in eve…