License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.AofA.2022.7
URN: urn:nbn:de:0030-drops-160930
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16093/
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Drmota, Michael ; Hainzl, Eva-Maria

Universal Properties of Catalytic Variable Equations

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LIPIcs-AofA-2022-7.pdf (0.7 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{drmota_et_al:LIPIcs.AofA.2022.7,
  author =	{Drmota, Michael and Hainzl, Eva-Maria},
  title =	{{Universal Properties of Catalytic Variable Equations}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16093},
  URN =		{urn:nbn:de:0030-drops-160930},
  doi =		{10.4230/LIPIcs.AofA.2022.7},
  annote =	{Keywords: catalytic equation, singular expansion, univeral asymptotics}
}

Keywords: catalytic equation, singular expansion, univeral asymptotics
Collection: 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)
Issue Date: 2022
Date of publication: 08.06.2022


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