## 230 Citations

Randomizing and Describing Groups

- Psychology
- 2017

In this work we study some topics in logic and group theory, and naturally, their intersection. One important theme in this work is the notion of random groups, which is informally the study of “what…

Combinatorial categories and permutation groups

- Mathematics, Computer ScienceArs Math. Contemp.
- 2016

It is shown how to enumerate regular objects in various categories with a given finite automorphism group G, how to represent them all as quotients of a single regular object U ( G ) , and how the outer automorphist group of Γ acts on them.

A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics

- Mathematics
- 2012

This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its…

CARRIER GRAPHS FOR REPRESENTATIONS OF THE RANK TWO FREE GROUP INTO ISOMETRIES OF HYPERBOLIC THREE SPACE

- Mathematics
- 2018

Carrier graphs were first introduced for closed hyperbolic 3-manifolds by White. In this paper, we first generalize this definition to carrier graphs for representations of a rank two free group into…

Regular dessins with a given automorphism group

- Mathematics
- 2013

Dessins d'enfants are combinatorial structures on compact Riemann surfaces defined over algebraic number fields, and regular dessins are the most symmetric of them. If G is a finite group, there are…

Self-duality of the compactified Ruijsenaars–Schneider system from quasi-Hamiltonian reduction

- Physics, Mathematics
- 2012

STACS 99

- Computer ScienceLecture Notes in Computer Science
- 2002

This exposition presents a model to formally study algorithms in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest, and demonstrates how some of the techniques of mechanism design can be applied towards distributed computation problems.

Kleinian groups with singly cusped parabolic fixed points

- Mathematics
- 2001

We consider geometrically innnite Kleinian groups and, in particular, groups with singly cusped parabolic xed points. In order to distinguish between diierent geometric characteristics of such…

Test words, generic elements and almost primitivity

- Mathematics
- 1999

A test element in a group G is an element g with the property that if f(g) = g for an endomorphism f of G to G then f must be an automorphism. A test element in a free group is called a test word.…

Commutators in Free Groups

- MathematicsCanadian Mathematical Bulletin
- 1981

We study the representations of an element of a free group as a commutator. For a given element g of a free group F, we are interested in the set of all pairs (x, y) of elements of F such that (1)…