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

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.

16 pages, 1 figure, 1 table. This article supersedes arXiv:1210.3425