We investigate the cogrowth and distribution of geodesics in R. Thompson's group F .
We compute the cogrowth series for Baumslag-Solitar groups BS(N, N) = a, b|a N b = ba N , which we show to be D-finite. It follows that their cogrowth rates are algebraic numbers.
Rotation distance between rooted binary trees measures the degree of similarity of two trees with ordered leaves and is equivalent to edge-flip distance between triangular subdivisions of regular polygons. There are no known polynomial-time algorithms for computing rotation distance. Existence of common edges makes computing rotation distance more… (More)