Tamari Lattices and the symmetric Thompson monoid

Details Tamari Lattices and the symmetric Thompson monoid Tamari Lattices and the symmetric Thompson monoid

2011-09-24

arxiv.org/abs/1109.5296v1

Mathematics

Combinatorics

35pages

Scientific paper

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.

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