Browsing University of Waterloo by Subject "Enumeration"
Now showing items 1-5 of 5
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Algebraic Methods and Monotone Hurwitz Numbers
(University of Waterloo, 2012-09-21)We develop algebraic methods to solve join-cut equations, which are partial differential equations that arise in the study of permutation factorizations. Using these techniques, we give a detailed study of the recently ... -
The combinatorics of the Jack parameter and the genus series for topological maps
(University of Waterloo, 2009-08-19)Informally, a rooted map is a topologically pointed embedding of a graph in a surface. This thesis examines two problems in the enumerative theory of rooted maps. The b-Conjecture, due to Goulden and Jackson, predicts ... -
Cyclic Sieving Phenomenon of Promotion on Rectangular Tableaux
(University of Waterloo, 2012-09-28)Cyclic sieving phenomenon (CSP) is a generalization by Reiner, Stanton, White of Stembridge's q=-1 phenomenon. When CSP is exhibited, orbits of a cyclic action on combinatorial objects show a nice structure and their sizes ... -
Enumerative Applications of Integrable Hierarchies
(University of Waterloo, 2015-05-21)Countably infinite families of partial differential equations such as the Kadomtzev - Petviashvili (KP) hierarchy and the B-type KP (BKP) hierarchy have received much interest in the mathematical and theoretical physics ... -
Parameterized Enumeration of Neighbour Strings and Kemeny Aggregations
(University of Waterloo, 2013-08-30)In this thesis, we consider approaches to enumeration problems in the parameterized complexity setting. We obtain competitive parameterized algorithms to enumerate all, as well as several of, the solutions for two related ...