2024-03-28T21:31:33Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1550932021-08-30T18:20:32Zoai_pmh:all155093
https://hdl.handle.net/2286/R.I.40773
http://rightsstatements.org/vocab/InC/1.0/
All Rights Reserved
2016
vii, 102 pages : illustrations (some color)
Doctoral Dissertation
Academic theses
Text
eng
Treat, Kevin
Fishel, Susanna
Czygrinow, Andrzej
Jones, John
Childress, Nancy
Colbourn, Charles
Arizona State University
Partial requirement for: Ph.D., Arizona State University, 2016
Includes bibliographical references (pages 99-100)
Field of study: Mathematics
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. <br/><br/>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.
Mathematics
Catalan lattice
Higher Stasheff-Tamari order
Tamari lattice
Lattice theory
On chains in the Tamari lattice