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Analytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumeration

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dc.contributor.authorMelczer, Stephen
dc.date.accessioned2017-06-26T15:53:10Z
dc.date.available2017-06-26T15:53:10Z
dc.date.issued2017-06-26
dc.date.submitted2017-06-20
dc.description.abstractThe field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of deep and powerful tools with applications across mathematics and the natural sciences. In addition to the now classical univariate theory, recent work in the study of analytic combinatorics in several variables (ACSV) has shown how to derive asymptotics for the coefficients of certain D-finite functions represented by diagonals of multivariate rational functions. This thesis examines the methods of ACSV from a computer algebra viewpoint, developing rigorous algorithms and giving the first complexity results in this area under conditions which are broadly satisfied. Furthermore, this thesis gives several new applications of ACSV to the enumeration of lattice walks restricted to certain regions. In addition to proving several open conjectures on the asymptotics of such walks, a detailed study of lattice walk models with weighted steps is undertaken.en
dc.identifier.urihttp://hdl.handle.net/10012/12039
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectAnalytic Combinatoricsen
dc.subjectEnumerative Combinatoricsen
dc.subjectSingularity Analysisen
dc.subjectComputer Algebraen
dc.subjectLattice Pathsen
dc.subjectRational Diagonalsen
dc.subjectPolynomial Systemsen
dc.titleAnalytic Combinatorics in Several Variables: Effective Asymptotics and Lattice Path Enumerationen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws.comment.hiddenUpdated after additional requested revisions by Alexis Le (removed sections 1.3.3 and 1.3.4). This thesis is for a co-tutelle PhD with a French school and therefore contains a summary chapter in French.en
uws.contributor.advisorLabahn, George
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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