C. Roney‐Dougal

collaborators

5 papers

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 $Sym (I^c ◯)$ is a sequence of elements of $I^c ◯$ with trivial pointwise stabiliser. The size of the smallest base for $G$ is denoted $b (G)$ . There…

math.CO2025

Regular bipartite multigraphs have many (but not too many) symmetries

Peter J. Cameron, Coen del Valle, Colva M. Roney-Dougal

Let $k$ and $l$ be integers, both at least 2. A $(k, l)$ -bipartite graph is an $l$ -regular bipartite multigraph with coloured bipartite sets of size $k$ . Define $I ¨ (k, l)$ and $Î¼(k,…

math.GR2025

Irredundant bases for soluble groups

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

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

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 $I^c ◯$ is a subset $B$ of $I^c ◯$ whose pointwise stabiliser $G_{(B)}$ is trivial. There is a natural greedy algor…

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…