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 combinator...
Other Authors: | |
---|---|
Format: | Doctoral Thesis |
Language: | English |
Published: |
2016
|
Subjects: | |
Online Access: | http://hdl.handle.net/2286/R.I.40773 |
id |
ndltd-asu.edu-item-40773 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-asu.edu-item-407732018-06-22T03:07:55Z 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 Treat, 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) Mathematics Catalan lattice Higher Stasheff-Tamari order Tamari lattice eng 110 pages Doctoral Dissertation Mathematics 2016 Doctoral Dissertation http://hdl.handle.net/2286/R.I.40773 http://rightsstatements.org/vocab/InC/1.0/ All Rights Reserved 2016 |
collection |
NDLTD |
language |
English |
format |
Doctoral Thesis |
sources |
NDLTD |
topic |
Mathematics Catalan lattice Higher Stasheff-Tamari order Tamari lattice |
spellingShingle |
Mathematics Catalan lattice Higher Stasheff-Tamari order Tamari lattice On Chains in the Tamari Lattice |
description |
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 |
author2 |
Treat, Kevin (Author) |
author_facet |
Treat, Kevin (Author) |
title |
On Chains in the Tamari Lattice |
title_short |
On Chains in the Tamari Lattice |
title_full |
On Chains in the Tamari Lattice |
title_fullStr |
On Chains in the Tamari Lattice |
title_full_unstemmed |
On Chains in the Tamari Lattice |
title_sort |
on chains in the tamari lattice |
publishDate |
2016 |
url |
http://hdl.handle.net/2286/R.I.40773 |
_version_ |
1718701304704925696 |