Algorithms for Bivariate Singularity Analysis.

Format:

Book

Thesis/Dissertation

Author/Creator:

DeVries, Timothy (Timothy John)

Contributor:

Pemantle, Robin, advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Mathematics.

Applied mathematics.

0364.

0405.

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

0364.

0405.

Physical Description:

135 pages

Contained In:

Dissertation Abstracts International 72-09B.

System Details:

Mode of access: World Wide Web.

text file

Summary:

An algorithm for bivariate singularity analysis is developed. For a wide class of bivariate, rational functions F = P/Q, this algorithm produces rigorous numerics for the asymptotic analysis of the Taylor coefficients of F at the origin. The paper begins with a self-contained treatment of multivariate singularity analysis. The analysis itself relies heavily on the geometry of the pole set VQ of F with respect to a height function h. This analysis is then applied to obtain asymptotics for the number of bicolored supertrees, computed in a purely multivariate way. This example is interesting in that the asymptotics can not be computed directly from the standard formulas of multivariate singularity analysis. Motivated by the topological study required by this example, we present characterization theorems in the bivariate case that classify the geometric features salient to the analysis. These characterization theorems are then used to produce an algorithm for this analysis in the bivariate case. A full implementation of the algorithm follows.

Notes:

Thesis (Ph.D. in Mathematics) -- University of Pennsylvania, 2011.

Source: Dissertation Abstracts International, Volume: 72-09, Section: B, page: 5334.

Adviser: Robin Pemantle.

Local Notes:

School code: 0175.

ISBN:

9781124732275

Access Restriction:

Restricted for use by site license.