English
Related papers

Related papers: Conjugacy problem in T-RAAGs

200 papers

We give an algorithm to solve the Conjugacy Problem for ascending HNN-extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group endomorphisms.

Group Theory · Mathematics 2025-10-08 Alan D. Logan

We examine the construction of Huang and Osajda that was used in their proof of the biautomaticity of Artin groups of almost large type. We describe a slightly simpler variant of that biautomatic structure, with explicit descriptions of a…

Group Theory · Mathematics 2018-07-10 Sarah Rees , Derek Holt

Given a graph $\Gamma$, the right-angled Artin group $A(\Gamma)$ is given by the presentation $\langle u \in V(\Gamma) \mid [u,v]=1, \ \{u,v\} \in E(\Gamma) \rangle$. The Embedding Problem in right-angled Artin groups asks, given two finite…

Group Theory · Mathematics 2023-04-12 Anthony Genevois

We solve the simultaneous conjugacy problem in Artin's braid groups and, more generally, in Garside groups, by means of a complete, effectively computable, finite invariant. This invariant generalizes the one-dimensional notion of super…

Group Theory · Mathematics 2018-02-16 Arkadius Kalka , Boaz Tsaban , Gary Vinokur

In this article, we solve the twisted conjugacy problem for solvable Baumslag--Solitar groups $BS(n,1)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(n,1)$ and an automorphism $\varphi \in \Aut(BS(n,1))$, decides…

Group Theory · Mathematics 2025-08-07 Oorna Mitra , Mallika Roy , Enric Ventura

The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…

Optimization and Control · Mathematics 2025-04-01 Rongxuan Li

There does not exist an algorithm that can determine whether or not a group presented by commutators is a right-angled Artin group.

Group Theory · Mathematics 2019-05-08 Martin R Bridson

Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the…

Geometric Topology · Mathematics 2007-05-23 Ki Hyoung Ko , Jang Won Lee

We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the…

Group Theory · Mathematics 2007-05-23 Elie Feder

We provide two alternative ways to determine the number of (bi-)twisted conjugacy classes in a finite group: one by counting certain irreducible characters and one by counting certain twisted conjugacy classes of other endomorphisms. In…

Group Theory · Mathematics 2026-03-03 Pieter Senden , Sam Tertooy

(Free-abelian)-by-free, self-similar groups generated by finite self-similar sets of tree automorphisms and having unsolvable conjugacy problem are constructed. Along the way, orbit undecidable, free subgroups of GL_d(Z), for d > 5, and…

Group Theory · Mathematics 2012-05-14 Zoran Sunic , Enric Ventura

We classify two-dimensional right-angled Coxeter groups that are quasiisometric to a right-angled Artin group defined by a tree, and show that when this is true the right-angled Coxeter group actually contains a visible finite index…

Group Theory · Mathematics 2025-11-12 Christopher H. Cashen

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…

Group Theory · Mathematics 2018-02-22 Jonathan Gryak , Robert M. Haralick , Delaram Kahrobaei

We construct a class of finitely generated groups which have arbitrarily large conjugacy separability function, but in which the conjugacy problem can be solved in polynomial time, demonstrating that the McKinsey algorithm for the conjugacy…

Group Theory · Mathematics 2025-04-17 Lukas Vandeputte

We have proved in [Topology, 45 1 (2006)] that fundamental groups of oriented geometrizable 3-manifolds have a solvable conjugacy problem. We now consider the case of groups of non-oriented geometrizable 3-manifolds in order to conclude…

Group Theory · Mathematics 2007-05-23 Jean-Philippe Preaux

Weanalyzethecomputationalcomplexityofanalgorithmtosolve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most…

Group Theory · Mathematics 2019-03-27 Jonathan Gryak , Delaram Kahrobaei , Conchita Martinez-Perez

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

Group Theory · Mathematics 2012-05-01 Alexander Fel'shtyn , Evgenij Troitsky

We construct two practical algorithms for twisted conjugacy classes of polycyclic-by-finite groups. The first algorithm determines whether two elements of a group are twisted conjugate for two given endomorphisms, under the condition that…

Group Theory · Mathematics 2021-10-22 Karel Dekimpe , Sam Tertooy

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.

Logic · Mathematics 2019-08-16 Samuel Coskey , Paul Ellis

A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an…

Group Theory · Mathematics 2025-04-01 Yu-Chan Chang , Lorenzo Ruffoni