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 \( {F^+_{\rm sym}} \)whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice meet and join are the counterparts of the least common multiple and greatest common divisor operations in \( {F^+_{\rm sym}} \). 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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Dehornoy, P. (2012). Tamari Lattices and the Symmetric Thompson Monoid. In: Müller-Hoissen, F., Pallo, J., Stasheff, J. (eds) Associahedra, Tamari Lattices and Related Structures. Progress in Mathematics, vol 299. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0405-9_11
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DOI: https://doi.org/10.1007/978-3-0348-0405-9_11
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