{"id":{"repo_id":"penn","oai_identifier":"oai:repository.upenn.edu:20.500.14332/30264"},"canonical_url":"https://search.dev.ndltd.org/etd/penn/oai:repository.upenn.edu:20.500.14332/30264","repository":{"repo_id":"penn","name":"University of Pennsylvania","base_url":"https://repository.upenn.edu/server/oai/request"},"display":{"title":"Algorithms for Bivariate Singularity Analysis","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["DeVries, Timothy"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Robin Pemantle"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-16","date_published":"2011-05-16","updated_at":"2026-07-24T03:46:44Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.upenn.edu/handle/20.500.14332/30264","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Robin Pemantle"]},{"key":"dc:creator","label":"Author","values":["DeVries, Timothy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-17T06:04:20.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-05-22T17:36:24Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-04-21T00:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-05-16"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation/Thesis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repository.upenn.edu/handle/20.500.14332/30264"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy (PhD)"]},{"key":"dc:title","label":"Title","values":["Algorithms for Bivariate Singularity Analysis"]}]}],"canonical_facts":{"dc:contributor.advisor":["Robin Pemantle"],"dc:creator":["DeVries, Timothy"],"dc:date":["2023-05-17T06:04:20.000"],"dc:date.accessioned":["2023-05-22T17:36:24Z"],"dc:date.available":["2011-04-21T00:00:00Z"],"dc:date.issued":["2011-05-16"],"dc:description.abstract":["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."],"dc:description.degree":["Doctor of Philosophy (PhD)"],"dc:identifier.uri":["https://repository.upenn.edu/handle/20.500.14332/30264"],"dc:title":["Algorithms for Bivariate Singularity Analysis"],"dc:type":["Dissertation/Thesis"]},"updated_at":"2026-07-24T03:46:44Z"}