Restricted rotation distance between k-ary trees Vol. 27, no. 1, pp. 19-33, 2023. Regular paper. Abstract We study restricted rotation distance between ternary and higher-valence trees using approaches based upon generalizations of Thompson's group $F$. We obtain bounds and a method for computing these distances exactly in linear time, as well as a linear-time algorithm for computing rotations needed to realize these distances. Unlike the binary case, the higher-valence notions of rotation distance do not give Tamari lattices, so there are fewer tools for analysis in the higher-valence settings. Higher-valence trees arise in a range of database and filesystem applications where balance is important for efficient performance.  This work is licensed under the terms of the CC-BY license. Submitted: June 2022. Reviewed: July 2022. Revised: December 2022. Accepted: February 2023. Final: February 2023. Published: February 2023. Communicated by Giuseppe Liotta article (PDF) BibTeX