2026-07-22T06:25:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16093 2024-03-06T10:56:56Z ddc:004 open_access

Universal Properties of Catalytic Variable Equations Drmota, Michael Hainzl, Eva-Maria catalytic equation singular expansion univeral asymptotics Catalytic equations appear in several combinatorial applications, most notably in the enumeration of lattice paths and in the enumeration of planar maps. The main purpose of this paper is to show that under certain positivity assumptions the dominant singularity of the solution function has a universal behavior. We have to distinguish between linear catalytic equations, where a dominating square-root singularity appears, and non-linear catalytic equations, where we - usually - have a singularity of type 3/2. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Michael Drmota and Eva-Maria Hainzl 2022 Is Part Of LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AofA.2022.7 urn:nbn:de:0030-drops-160930 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.7 eng https://creativecommons.org/licenses/by/4.0/legalcode