2026-05-23T03:10:11Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1553402024-12-20T18:25:12Zoai_pmh:alloai_pmh:repo_items155340
https://hdl.handle.net/2286/R.I.43994
http://rightsstatements.org/vocab/InC/1.0/
All Rights Reserved
2017
viii, 140 pages : illustrations
Doctoral Dissertation
Academic theses
Text
eng
Al-Suleiman, Sultan
Fishel, Susanna
Childress, Nancy
Czygrinow, Andrzej
Jones, John
Spielberg, John
Arizona State University
Partial requirement for: Ph.D., Arizona State University, 2017
Includes bibliographical references (pages 137-140)
Field of study: Mathematics
The Cambrian lattice corresponding to a Coxeter element c of An, denoted Camb(c),<br/><br/>is the subposet of An induced by the c-sortable elements, and the m-eralized Cambrian<br/><br/>lattice corresponding to c, denoted Cambm(c), is dened as a subposet of the<br/><br/>braid group accompanied with the right weak ordering induced by the c-sortable elements<br/><br/>under certain conditions. Both of these families generalize the well-studied<br/><br/>Tamari lattice Tn rst introduced by D. Tamari in 1962. S. Fishel and L. Nelson<br/><br/>enumerated the chains of maximum length of Tamari lattices.<br/><br/>In this dissertation, I study the chains of maximum length of the Cambrian and<br/><br/>m-eralized Cambrian lattices, precisely, I enumerate these chains in terms of other<br/><br/>objects, and then nd formulas for the number of these chains for all m-eralized<br/><br/>Cambrian lattices of A1, A2, A3, and A4. Furthermore, I give an alternative proof<br/><br/>for the number of chains of maximum length of the Tamari lattice Tn, and provide<br/><br/>conjectures and corollaries for the number of these chains for all m-eralized Cambrian<br/><br/>lattices of A5.
Mathematics
Cambrian Lattices
Lattices
Maximal Chains
m-eralized Cambrian Lattices
Tamari Lattices
Lattice theory
Toward enumerating the chains of maximum length of Cambrian and m-eralized Cambrian lattices