Tamari Lattices and the symmetric Thompson monoid
Combinatorics
2011-09-27 v1 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1109.5296,
title = {Tamari Lattices and the symmetric Thompson monoid},
author = {Patrick Dehornoy},
journal= {arXiv preprint arXiv:1109.5296},
year = {2011}
}
Comments
35pages