7 citations · 12 across the 6 of their papers we have counts for
6 papers
On groups whose cogrowth series is the diagonal of a rational series
Alex Bishop
We show that if a group contains as a finite-index subgroup, then its cogrowth series is the diagonal of a rational function for every generating set. Thi…
A virtually 2-step nilpotent group with polynomial geodesic growth
Alex Bishop, Murray Elder
A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until…
Density of Metric Small Cancellation in Finitely Presented Groups
Alex Bishop, Michal Ferov
Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously know…
Geodesic growth in virtually abelian groups
Alex Bishop
We show that the geodesic growth function of any finitely generated virtually abelian group is either polynomial or exponential; and that the geodesic growth series is holonomic, a…
Bounded Automata Groups are co-ET0L
Alex Bishop, Murray Elder
Holt and Röver proved that finitely generated bounded automata groups have indexed co-word problem. Here we sharpen this result to show they are in fact co-ET0L.
Consistent Approximation of Epidemic Dynamics on Degree-heterogeneous Clustered Networks
A. Bishop, I. Z. Kiss, T. House
Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clusterin…