TAMARI LATTICES AND THE SYMMETRIC THOMPSON MONOID

Abstract. We investigate the connection between Tamari lattices and the Thomp-son group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this corre-spondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length ` chain in the nth Tamari lattice whose endpoints are at distance at most 12`/n. 1