Description
The Cambrian lattice corresponding to a Coxeter element c of An, denoted Camb(c),
is the subposet of An induced by the c-sortable elements, and the m-eralized Cambrian
lattice corresponding to c, denoted Cambm(c), is dened as a subposet of the
braid group accompanied with the right weak ordering induced by the c-sortable elements
under certain conditions. Both of these families generalize the well-studied
Tamari lattice Tn rst introduced by D. Tamari in 1962. S. Fishel and L. Nelson
enumerated the chains of maximum length of Tamari lattices.
In this dissertation, I study the chains of maximum length of the Cambrian and
m-eralized Cambrian lattices, precisely, I enumerate these chains in terms of other
objects, and then nd formulas for the number of these chains for all m-eralized
Cambrian lattices of A1, A2, A3, and A4. Furthermore, I give an alternative proof
for the number of chains of maximum length of the Tamari lattice Tn, and provide
conjectures and corollaries for the number of these chains for all m-eralized Cambrian
lattices of A5.
is the subposet of An induced by the c-sortable elements, and the m-eralized Cambrian
lattice corresponding to c, denoted Cambm(c), is dened as a subposet of the
braid group accompanied with the right weak ordering induced by the c-sortable elements
under certain conditions. Both of these families generalize the well-studied
Tamari lattice Tn rst introduced by D. Tamari in 1962. S. Fishel and L. Nelson
enumerated the chains of maximum length of Tamari lattices.
In this dissertation, I study the chains of maximum length of the Cambrian and
m-eralized Cambrian lattices, precisely, I enumerate these chains in terms of other
objects, and then nd formulas for the number of these chains for all m-eralized
Cambrian lattices of A1, A2, A3, and A4. Furthermore, I give an alternative proof
for the number of chains of maximum length of the Tamari lattice Tn, and provide
conjectures and corollaries for the number of these chains for all m-eralized Cambrian
lattices of A5.
Details
Title
- Toward enumerating the chains of maximum length of Cambrian and m-eralized Cambrian lattices
Contributors
- Al-Suleiman, Sultan (Author)
- Fishel, Susanna (Thesis advisor)
- Childress, Nancy (Committee member)
- Czygrinow, Andrzej (Committee member)
- Jones, John (Committee member)
- Spielberg, John (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2017
Subjects
Resource Type
Collections this item is in
Note
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thesisPartial requirement for: Ph.D., Arizona State University, 2017
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bibliographyIncludes bibliographical references (pages 137-140)
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Field of study: Mathematics
Citation and reuse
Statement of Responsibility
by Sultan Al-Suleiman