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On Chains in the Tamari Lattice

abstract: The Tamari lattice T(n) was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Since then it has been studied in various areas of mathematics including cluster algebras, discrete geometry, algebraic combinatorics, and Catalan theory. Although in several related lattices the number of maximal chains is known, the enumeration of these chains in Tamari lattices is still an open problem.

This dissertation defines a partially-ordered set on equivalence classes of certain saturated chains of T(n) called the Tamari Block poset, TB(lambda). It further proves TB(lambda) is a graded lattice. It then shows for lambda = (n-1,...,2,1) TB(lambda) is anti-isomorphic to the Higher Stasheff-Tamari orders in dimension 3 on n+2 elements. It also investigates enumeration questions involving TB(lambda), and proves other structural results along the way. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2016

Identiferoai:union.ndltd.org:asu.edu/item:40773
Date January 2016
ContributorsTreat, Kevin (Author), Fishel, Susanna (Advisor), Czygrinow, Andrzej (Committee member), Jones, John (Committee member), Childress, Nancy (Committee member), Colbourn, Charles (Committee member), Arizona State University (Publisher)
Source SetsArizona State University
LanguageEnglish
Detected LanguageEnglish
TypeDoctoral Dissertation
Format110 pages
Rightshttp://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved

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