A natural, but slowly emerging program. In his PhD thesis prepared under the supervision of
Graham Higman and defended in 1965 [123], and in the article that followed [124], FA …

Fascinating connections exist between group theory and automata theory, and a wide
variety of them are discussed in this text. Automata can be used in group theory to encode …

In this article we study domino snake problems on finitely generated groups. We provide
general properties of these problems and introduce new tools for their study. The first is the …

Artin groups of large type are shortlex automatic with regular geodesics Page 1 Proc.
London Math. Soc. (3) 104 (2012) 486–512 Cо2011 London Mathematical Society doi:10.1112/plms/pdr035 …

We consider the Artin groups of dihedral type I2 (k) defined by the presentation Ak=〈 a, b|
prod (a, b; k)= prod (b, a; k)〉 where prod (s, t; k)= ststs…, with k terms in the product on the …

We prove that in the Cayley graph of any braid group modulo its center $ B_n/Z (B_n) $,
equipped with Garside's generating set, the axes of all pseudo-Anosov braids are strongly …

We study the regularity of several languages derived from conjugacy classes in a finitely
generated group G for a variety of examples including word hyperbolic, virtually abelian …

A subshift of finite type is a set of tilings of a group subject to a finite number of local
constraints, where the group acts by translation. In recent years, much progress has been …

We describe new types of normal forms for braid monoids, Artin–Tits monoids, and, more
generally, for all monoids in which divisibility has some convenient lattice properties (“locally …

We prove that generic elements of braid groups are pseudo-Anosov, in the following sense:
in the Cayley graph of the braid group with n> 3 strands, with respect to Garside's generating …