On higher q, t-Catalan numbers

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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.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2014
Issuance monographic
Language English


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-


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

© 2014 by Yuncheng Lin
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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