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arXiv · 1608.06703

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

Murray Elder·Cameron Rogers
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Abstract

We critically analyse a recent numerical method due to the first author, Rechnitzer and van Rensburg, which attempts to detect amenability or non-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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Murray Elder, Cameron Rogers. 2016-08-24. Sub-dominant cogrowth behaviour and the viability of deciding amenability numerically. https://arxiv.org/abs/1608.06703

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