abstract: 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. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2017
| Identifer | oai:union.ndltd.org:asu.edu/item:43994 |
| Date | January 2017 |
| Contributors | AL-SULEIMAN, SULTAN (Author), Fishel, Susanna (Advisor), Childress, Nancy (Committee member), Czygrinow, Andrzej (Committee member), Jones, John (Committee member), Spielberg, John (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Doctoral Dissertation |
| Format | 149 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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