C. Roney‐Dougal

activity

20172026

most citedOn random presentations with fixed relator length

2 citations · 3 across the 7 of their papers we have counts for

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math.GR2026

Greedy bases and relational complexity of diagonal type groups

Hong Yi Huang, Colva M. Roney-Dougal

A base for a subgroup $G$ of $Sym (Ω)$ is a sequence of elements of $Ω$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b (G)$ . There is…

math.GR2025

On Cameron's Greedy Conjecture

Coen del Valle, Colva M. Roney-Dougal

A base for a permutation group $G$ acting on a set $Ω$ is a subset $B$ of $Ω$ whose pointwise stabiliser $G_{(B)}$ is trivial. There is a natural greedy algorit…

math.GR2025

Subgroups of symmetric groups: enumeration and asymptotic properties

Colva M. Roney-Dougal, Gareth Tracey

In this paper, we prove that the symmetric group $S_{n}$ has $2^{n^{2} /16 + o (n^{2})}$ subgroups, settling a conjecture of Pyber from 1993. We also derive asymptotically sharp upp…

math.GR2025

Irredundant bases for soluble groups

Sofia Brenner, Coen del Valle, Colva M. Roney-Dougal

Let $Δ$ be a finite set and $G$ be a subgroup of $Sym (Δ)$ . An irredundant base for $G$ is a sequence of points of $Δ$ yielding a strictly descending chain of pointwi…

math.GR2023

The relational complexity of linear groups acting on subspaces

Saul D. Freedman, Veronica Kelsey, Colva M. Roney-Dougal

The relational complexity of a subgroup $G$ of $Sym (Ω)$ is a measure of the way in which the orbits of $G$ on $Ω^{k}$ for various $k$ determine the original action of $G$ . V…

math.GR2023

Irredundant bases for the symmetric group

Colva M. Roney-Dougal, Peiran Wu

An irredundant base of a group $G$ acting faithfully on a finite set $Γ$ is a sequence of points in $Γ$ that produces a strictly descending chain of pointwise stabiliser subgroups…