The cogrowth series for BS(N,N) is D-finite

2013/09/30 by M. Elder, A. Rechnitzer, E. J. Janse van Rensburg +1
Mathematics · #math.GR #math.CO #msc:20F69 #msc:20F65 #msc:05A15

paper · pdf · doi:10.1142/s0218196714500106

published as International Journal of Algebra and Computation 24 (2014) Issue 2 pages 171-187 · 16 pages, 1 figure, 1 table. This article supersedes arXiv:1210.3425

arxiv created 2013/12/20 · arxiv updated 2014/06/09

Abstract

We compute the cogrowth series for Baumslag-Solitar groups 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.

Citations

• On trivial words in finitely presented groups