Tamari Lattices and the symmetric Thompson monoid

Patrick Dehornoy (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We investigate the connection between Tamari lattices and the Thompson 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 correspondence, 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 l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.

Mots clés: Tamari lattice; Thompson groups; group of fractions; least common multiple; greatest common divisor; subword reversing

Domaines: Combinatoire [math.CO]; Théorie des groupes [math.GR]

Patrick Dehornoy. Tamari Lattices and the symmetric Thompson monoid. 2011. ⟨hal-00626262⟩