The q-catalan numbers of Macmahon and a related identity of Andrews
Open Access
Author:
Cobern, Sara Catherine
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Ae Ja Yee, Thesis Supervisor Victoria V Sadovskaya, Thesis Honors Advisor
Keywords:
q-Catalan numbers Mathematics Combinatorics
Abstract:
This thesis offers a look into the q-Catalan numbers of MacMahon and their properties. The beginning of the paper explains the Catalan numbers and the lattice path interpretation of them. We then move to the generalized version of the Catalan numbers, the q-Catalan numbers. Much of the work provided in this thesis is related to George E. Andrews' paper titled "q-Catalan Identities." Some of the problems proposed at the end of his paper are answered in this thesis, and the work leading up to those solutions is provided.
