Right arm rotation and a subposet of the Tamari lattice

The comb poset is a subposet of the Tamari lattice introduced by J.M. Pallo. While the comb poset is not a lattice, its intervals have a number of nice properties. I will talk a bit about tree rotation and the comb poset in general and then about meets and joins (when they exist) in the comb poset, the rotation distance between two trees that lie in an interval of the comb poset and the original motivation for our work on the comb poset, namely parsewords and the Four Color Theorem.