3 papers
math.GR2026
Synchronizing groups and weakly perfect graphs: a survey
Peter J. Cameron
The concept of synchronization has been transferred from finite automata, via transformation semigroups, to permutation groups: a permutation group on a finite set is said…
math.CO2025
Hall's marriage theorem
Peter J. Cameron
In 1935, Philip Hall published what is often referred to as ``Hall's marriage theorem'' in a short paper (P.~Hall, On Representatives of Subsets, \textit{J. Lond. Math. Soc.} (1) \…
math.CO2024
Simplicial complexes defined on groups
Peter J. Cameron
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes…