Tamari lattices and noncrossing partitions in type B Original Research Article

The usual, or type image, Tamari lattice is a partial order on image, the triangulations of an image-gon. We define a partial order on image, the set of centrally symmetric triangulations of a image-gon. We show that it is a lattice, and that it shares certain other nice properties of the image Tamari lattice, and therefore that it deserves to be considered the image Tamari lattice. We also define a bijection between image and the noncrossing partitions of type image defined by Reiner.