Full Record

New Search | Similar Records

Author
Title Kazhdan-Lusztig Polynomials of Matroids and Their Roots
URL
Publication Date
Date Accessioned
Degree PhD
Discipline/Department Department of Mathematics
Degree Level doctoral
University/Publisher University of Oregon
Abstract The Kazhdan-Lusztig polynomial of a matroid M, denoted P_M( t ), was recently defined by Elias, Proudfoot, and Wakefield. These polynomials are analogous to the classical Kazhdan-Lusztig polynomials associated with Coxeter groups. For example, in both cases there is a purely combinatorial recursive definition. Furthermore, in the classical setting, if the Coxeter group is a Weyl group then the Kazhdan-Lusztig polynomial is a Poincare polynomial for the intersection cohomology of a particular variety; in the matroid setting, if M is a realizable matroid then the Kazhdan-Lusztig polynomial is also the intersection cohomology Poincare polynomial of a variety corresponding to M. (Though there are several analogies between the two types of polynomials, the theory is quite different.) Here we compute the Kazhdan-Lusztig polynomials of several graphical matroids, including thagomizer graphs, the complete bipartite graph K_{2,n}, and (conjecturally) fan graphs. Additionally, we investigate a conjecture by the author, Proudfoot, and Young on the real-rootedness for Kazhdan-Lusztig polynomials of these matroids as well as a conjecture on the interlacing behavior of these roots. We also show that the Kazhdan-Lusztig polynomials of uniform matroids of rank n − 1 on n elements are real-rooted. This dissertation includes both previously published and unpublished co-authored material.
Subjects/Keywords Kazhdan-Lusztig polynomials; Matroid theory; real-rootedness
Contributors Proudfoot, Nicholas (advisor)
Language en
Rights All Rights Reserved.
Country of Publication us
Record ID handle:1794/23913
Repository oregon
Date Retrieved
Date Indexed 2020-06-18
Grantor University of Oregon
Issued Date 2018-10-31 00:00:00

Sample Search Hits | Sample Images | Cited Works

…mathematically or otherwise. Thank you for your support and encouragement. Finally, I owe a huge debt of gratitude to my friends and all the people who have supported me during my time at the University of Oregon. It would be impossible to list the name of every…

.