Description
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.
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.
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Details
Title
- On chains in the Tamari lattice
Contributors
- Treat, Kevin (Author)
- Fishel, Susanna (Thesis advisor)
- Czygrinow, Andrzej (Committee member)
- Jones, John (Committee member)
- Childress, Nancy (Committee member)
- Colbourn, Charles (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2016
Resource Type
Collections this item is in
Note
- thesisPartial requirement for: Ph.D., Arizona State University, 2016
- bibliographyIncludes bibliographical references (pages 99-100)
- Field of study: Mathematics
Citation and reuse
Statement of Responsibility
by Kevin Treat