Sub-dominant cogrowth behaviour and the viability of deciding amenability numerically

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Journal Article
Experimental Mathematics, 2017
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We critically analyse 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.
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