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

preprint2013arXivOpen access

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

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

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