Related papers: Conjugacy languages in virtual graph products
Metrically homogeneous graphs are connected graphs which, when endowed with the path metric, are homogeneous as metric spaces. In this paper we introduce the concept of twisted automorphisms, a notion of isomorphism up to a permutation of…
We study the full language of quasigeodesics in Cayley graphs, with fixed error constants. We show that, given a non-virtually-cyclic nilpotent group or Baumslag--Solitar group, and any finite generating set, such languages fail to be…
We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Artin group, and, if so, producing a presentation graph for such…
In this paper, we study the asymptotics of several growth functions related to twisted conjugacy on virtually abelian groups. First, we study the twisted conjugacy growth function, which counts the number of twisted conjugacy classes…
In this paper, we construct an implementable algorithm which solves the conjugacy problem in twisted right-angled Artin groups (T-RAAGs). In certain cases, the complexity is known to be linear, by reducing the problem to the twisted…
It is shown that for graph groups (right-angled Artin groups) the conjugacy problem as well as a restricted version of the simultaneous conjugacy problem can be solved in polynomial time even if input words are represented in a compressed…
Let $G = K \rtimes \langle t \rangle $ be a finitely generated group where $K$ is abelian and $\langle t\rangle$ is the infinite cyclic group. Let $ R $ be a finite symmetric subset of $K$ such that $S = \{ (r,1),(0,t^{\pm 1}) \mid r \in R…
A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
In various occasions the conjugacy problem in finitely generated amalgamated products and HNN extensions can be decided efficiently for elements which cannot be conjugated into the base groups. This observation asks for a bound on how many…
In this paper we study the elementary theory of graph products of groups and show that under natural conditions on the vertex groups we can recover (the core of) the underlying graph and the associated vertex groups. More precisely, we…
Let $G$ be a hyperbolic group that splits as a graph of free groups with cyclic edge groups. We prove that, unless $G$ is isomorphic to a free product of free and surface groups, every finite abelian group $M$ appears as a direct summand in…
Virtual Artin groups were recently introduced by Bellingeri, Paris, and Thiel as broad generalizations of the well-known virtual braid groups. For each Coxeter graph $\Gamma$, they defined the virtual Artin group $VA[\Gamma]$, which is…
Human communication combines speech with expressive nonverbal cues such as hand gestures that serve manifold communicative functions. Yet, current generative gesture generation approaches are restricted to simple, repetitive beat gestures…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
A classical result of Schreier states that nontrivial finitely generated normal subgroups of free groups are of finite index, that is, free groups can only quotient to finite groups with finitely generated kernel. In this note we extend…
Embodied agents, in the form of virtual agents or social robots, are rapidly becoming more widespread. In human-human interactions, humans use nonverbal behaviours to convey their attitudes, feelings, and intentions. Therefore, this…
The automorphism group of the composition of graphs $G \circ H$ contains the wreath product $Aut(H) \wr Aut(G)$ of the automorphism groups of the corresponding graphs. The classical problem considered by Sabidussi and Hemminger was under…
We study isometric representations of product systems of correspondences over the semigroup $\mathbb{N}^k$ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal…
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…