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Universal Properties of Catalytic Variable Equations

Authors Michael Drmota , Eva-Maria Hainzl

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Author Details

Michael Drmota
  • TU Wien, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria
Eva-Maria Hainzl
  • TU Wien, Institute of Discrete Mathematics and Geometry, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria

Funding

  • Drmota, Michael: Research supported by the Austrian Science Foundation FWF, projects F50-02, F55-02, and P35016.
  • Hainzl, Eva-Maria: Research supported by the Austrian Science Foundation FWF, project F55-02.

Acknowledgements

We thank the referees for their careful reading and their valuable comments for improving the presentation.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.AofA.2022.7

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Generating functions
Keywords
  • catalytic equation
  • singular expansion
  • univeral asymptotics

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References

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