ABSTRACT
We critically analyze a recent numerical method due to the first author, Rechnitzer, and van Rensburg, which attempts to detect amenability in a finitely generated group by numerically estimating its asymptotic cogrowth rate. We identify two potential sources of error. We then propose a modification of the method that enables it to easily compute surprisingly accurate estimates for initial terms of the cogrowth sequence.
Acknowledgments
The authors wish to thank Andrew Rechnitzer, Andrew Elvey-Price, and the anonymous reviewer for helpful feedback on this work.