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DOI: 10.4230/LIPIcs.AofA.2022.7

Universal Properties of Catalytic Variable Equations

Authors: Michael Drmota and Eva-Maria Hainzl

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)

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.

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Michael Drmota and Eva-Maria Hainzl. Universal Properties of Catalytic Variable Equations. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.7},
  URN =		{urn:nbn:de:0030-drops-160930},
  doi =		{10.4230/LIPIcs.AofA.2022.7},
  annote =	{Keywords: catalytic equation, singular expansion, univeral asymptotics}
}

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Universal Properties of Catalytic Variable Equations

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