The cogrowth series for $\mathrm{BS}(N,N)$ is D-finite

A. Rechnitzer; E. J. Janse van Rensburg; M. Elder; T. Wong

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The cogrowth series for $\mathrm{BS}(N,N)$ is D-finite

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arxiv 1309.4184 v3 pith:YX7O2JNU submitted 2013-09-17 math.GR math.CO

M. Elder , A. Rechnitzer , E. J. Janse van Rensburg , T. Wong This is my paper

classification math.GRmath.CO

keywords cogrowthd-finitemathrmseriesalgebraicbaumslag-solitarcomputefollows

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abstract

We compute the cogrowth series for Baumslag-Solitar groups $\mathrm{BS}(N,N) = < a,b | a^N b = b a^N > $, which we show to be D-finite. It follows that their cogrowth rates are algebraic numbers.

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