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Title
Toward enumerating the chains of maximum length of Cambrian and m-eralized Cambrian lattices
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.
Date Created
2017
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)
Topical Subject
Resource Type
Extent
viii, 140 pages : illustrations
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.I.43994
Statement of Responsibility
by Sultan Al-Suleiman
Description Source
Retrieved on Sept. 12, 2017
Level of coding
full
Note
thesis
Partial requirement for: Ph.D., Arizona State University, 2017
bibliography
Includes bibliographical references (pages 137-140)
Field of study: Mathematics
System Created
- 2017-06-01 01:21:08
System Modified
- 2021-08-26 09:47:01
- 3 years 2 months ago
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