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MIT Combinatorics Seminar

Thompson Monoids and Tamari Lattices


Zoran Sunik (Texas A&M University)

Wednesday, April 26, 2006   4:30 PM   Building 2 Room 105 

ABSTRACT

A connection is exhibited between Thompson monoids and Tamari lattices. In the most basic case, it relates the positive monoid P of Thompson group F to Tamari lattices on finite Coxeter groups of type A regarded as lattices under the weak Bruhat order. The Tamari congruence classes correspond to classes of equivalent elements in P. The two well known normal forms in P correspond to endpoints of intervals in the weak Bruhat order that determine the Tamari classes. In the monoid P these correspond to the lexicographically largest and lexicographically smallest form, while on the level of permutations they correspond to 132-avoiding and 231-avoiding permutations.