A new proof of the growth rate of the solvable Baumslag–Solitar groups

We exhibit a regular language of geodesics for a large set of elements of BS(1, n) and show that the growth rate of this language is the growth rate of the group. This provides a straightforward calculation of the growth rate of BS(1, n), which was initially computed by Collins et al. (AM (Basel) 62:1-11, 1994). Our methods are based on those we develop in Taback and Walker (JTA, to appear) to show that BS(1, n) has a positive density of elements of positive, negative and zero conjugation curvature, as introduced by Bar-Natan et al. (JTA, 2020, https://doi.org/10.1142/S1793525321500096).