On higher q, t-Catalan numbers
Abstract/Contents
- Abstract
- The purpose of this thesis is two-fold: to give a self-contained evaluation of the symmetric function version of higher $q, t$-Catalan numbers $SC_n^{(m)}(q, t) = \langle \nabla^m e_n, e_n \rangle$ as a summation of rational functions of $q$ and $t$ indexed by partitions, and to prove the conjecture that the combinatorial version $WC_n^{(m)}(q, t)$ and the symmetric function version $SC_n^{(m)}(q, t)$ of higher $q, t$-Catalan numbers are equivalent for $n$ up to 6, thus strengthening a result of Lee, Li, and Loehr (see~\cite[Section 5]{LLL14}) which shows the equivalence for $n$ up to 4.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2014 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Lin, Yuncheng |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Vakil, Ravi |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Diaconis, Persi |
| Thesis advisor | Yun, Zhiwei, 1982- |
| Advisor | Diaconis, Persi |
| Advisor | Yun, Zhiwei, 1982- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Yuncheng Lin. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Yuncheng Lin
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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