3 problems

Let $(G_{1,1},X)$ be the group–space pair whose patterns are being studied, and let a pattern be a sequence encoded by parenthesized blocks; within a block, $(0,-1)$ or $(1,0)$ den…

Let $G$ be a word-hyperbolic group. An automatic structure for $G$ has property R when its accepting automaton is both undirected and Perron–Frobenius, meaning that the adjacency m…

Shephard groups' bi-automaticity conjecture. Every Shephard group is bi-automatic. The conjecture extends analogous conjectures for Artin and Coxeter groups. The paper proves it fo…