32 citations · 63 across the 20 of their papers we have counts for
10 papers · 1 filter
The average-case complexity of the Word Problem for groups of matrices over~ is linear
Frédérique Bassino, Cyril Nicaud, Vincent Jugé +1
We show that the Word Problem in finitely generated subgroups of can be solved in linear average-case complexity, both when the input words are chosen u…
Silhouettes and generic properties of subgroups of the modular group
Frédérique Bassino, Cyril Nicaud, Pascal Weil
We show that the probability for a finitely generated subgroup of the modular group, of size , to be almost malnormal or non-parabolic, tends to 0 as tends to infinity -- wh…
Random generation of subgroups of the modular group with a fixed isomorphism type
Frédérique Bassino, Cyril Nicaud, Pascal Weil
We show how to efficiently count and generate uniformly at random finitely generated subgroups of the modular group of a given isomorphism type. The me…
Silhouettes and generic properties of subgroups of the modular group
Frédérique Bassino, Cyril Nicaud, Pascal Weil
We show how to count and randomly generate finitely generated subgroups of the modular group of a given isomorphism type. We also prove that almost mal…
Statistics of subgroups of the modular group
Frédérique Bassino, Cyril Nicaud, Pascal Weil
We count the finitely generated subgroups of the modular group . More precisely: each such subgroup can be represented by its Stallings graph …
Random presentations and random subgroups: a survey
Frédérique Bassino, Cyril Nicaud, Pascal Weil
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a…
Generic properties of subgroups of free groups and finite presentations
Frédérique Bassino, Cyril Nicaud, Pascal Weil
Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects a…
On the genericity of Whitehead minimality
Frédérique Bassino, Cyril Nicaud, Pascal Weil
We show that a finitely generated subgroup of a free group, chosen uniformly at random, is strictly Whitehead minimal with overwhelming probability. Whitehead minimality is one of…
Statistical properties of subgroups of free groups
Frédérique Bassino, Armando Martino, Cyril Nicaud +2
The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based…
Random generation of finitely generated subgroups of a free group
Frédérique Bassino, Cyril Nicaud, Pascal Weil
We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertice…