Browsing University of Waterloo by Subject "enumeration"
Now showing items 1-10 of 10
-
Algorithms for Analytic Combinatorics in Several Variables
(University of Waterloo, 2023-04-25)Given a multivariate rational generating function we are interested in computing asymptotic formulas for the sequences encoded by the coefficients. In this thesis we apply the theory of analytic combinatorics in several ... -
Aspects of Quantum Field Theory in Enumerative Graph Theory
(University of Waterloo, 2022-10-24)While a quantum field theorist has many uses for mathematics of all kinds, the relationship between quantum field theory and mathematics is far too fluid in the world of modern research to be described as the simple provision ... -
Combinatorial aspects of braids with applications to cryptography
(University of Waterloo, 2015-08-25)This thesis is a collection of different results on braids, and draws connections between them. We first introduce braids by showcasing a number of equivalent ways of describing what a braid is, and how those representations ... -
Combinatorial Methods for Enumerating Maps in Surfaces of Arbitrary Genus
(University of Waterloo, 2016-06-10)The problem of map enumeration is one that has been studied intensely for the past half century. Early work on this subject included the works of Tutte for various types of rooted planar maps and the works of Brown for ... -
Core Structures in Random Graphs and Hypergraphs
(University of Waterloo, 2013-08-30)The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, ... -
Differential Equations and Depth First Search for Enumeration of Maps in Surfaces
(University of Waterloo, 1999)A map is an embedding of the vertices and edges of a graph into a compact 2-manifold such that the remainder of the surface has components homeomorphic to open disks. With the goal of proving the Four Colour Theorem, ... -
Enumerating matroid extensions
(University of Waterloo, 2023-09-01)This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ... -
Enumeration of Factorizations in the Symmetric Group: From Centrality to Non-centrality
(University of Waterloo, 2011-04-25)The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This ... -
Enumerative perspectives on chord diagrams
(University of Waterloo, 2022-10-07)The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ... -
Transitive Factorizations of Permutations and Eulerian Maps in the Plane
(University of Waterloo, 2005)The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800's. This problem translates combinatorially into factoring a permutation with a specified cycle ...