11 problems

Rivin's conjecture. The conjugacy growth series $\mathcal P(z)$ of $G$ is rational if and only if $G$ is virtually cyclic.

Let $(\Gamma,L)$ be an $n$-dimensional periodic graph, where $\Gamma$ is a directed graph, $L$ is a free abelian group of rank $n$ acting freely on $\Gamma$, and the quotient graph…

Let $h_{105}(x)$ be the coordinator polynomial of the lattice $\mathbb Z[\zeta_{105}]$ with respect to the set of all $105$th roots of unity. A polynomial is palindromic if its coe…

Let $\zeta_{15}=e^{2\pi i/15}$, and let $h_{15}(x)$ be the coordinator polynomial of the lattice $\mathbb Z[\zeta_{15}]$ with respect to the set of all $15$th roots of unity. Parke…

Let $p$ be an odd prime, let $\zeta_{2p}=e^{2\pi i/(2p)}$, and let $h_{2p}(x)$ be the coordinator polynomial of $\mathbb Z[\zeta_{2p}]$ with respect to the set of all $2p$th roots…

Let $m$ be a positive integer. Write $\sqrt m$ for the squarefree part of $m$, let $\zeta_m=e^{2\pi i/m}$, and let $h_m(x)$ be the coordinator polynomial of the lattice…

Let $B_3$ be the three-strand braid group, let $\Sigma_3^{\scriptstyle *}$ denote its dual generating set, and let $\mathcal{S}(B_3,\Sigma_3^{\scriptstyle *})$ and…

Let $G$ be a finitely generated acylindrically hyperbolic group, meaning a group acting non-elementarily and acylindrically by isometries on a hyperbolic space. Let…

Let $BS(p,q)=\langle a,t\mid ta^pt^{-1}=a^q\rangle$, and consider the growth series of its horocyclic subgroup, consisting of elements represented by powers of the generator $a$. F…

Let $G$ be a group with a finite generating set $S$, and let $\Omega(G,S)$ be Saito's set associated with the word-growth series of $(G,S)$. Saito's conjecture. If $G$ is a word hy…

Let a $p$-letter automaton generate a semigroup, let its growth series be the generating function recording the number of elements of each length, and let its dual be the automaton…