Record link: 
http://hdl.handle.net/20.500.12708/139401
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Title: 
Universal Properties of Catalytic Variable Equations
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Citation: 
Drmota, M., & Hainzl, E. M. (2022). Universal Properties of Catalytic Variable Equations. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022) (pp. 1–15). https://doi.org/10.4230/LIPIcs.AofA.2022.7
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Publisher DOI: 
10.4230/LIPIcs.AofA.2022.7
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Drmota, Michael 
Hainzl, Eva Maria 
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Organisational Unit: 
E104-05 - Forschungsbereich Kombinatorik und Algorithmen 
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Published in: 
33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022) 
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ISBN: 
9783959772303
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Volume: 
225
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Date (published): 
1-Jun-2022
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Event name: 
33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022) 
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Event date: 
20-Jun-2022 - 24-Jun-2022
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Event place: 
United States of America (the)
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Number of Pages: 
15
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Peer reviewed: 
Yes
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Keywords: 
catalytic equation; singular expansion; univeral asymptotics
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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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Project title: 
Unendliche singuläre Systeme und zufällig diskrete Objekte: P 35016-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) 
Formeigenschaften von planaren Karten und planare Graphen: F5002-N15 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) 
SFB-Teilprojekt: F5502-N26 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) 
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Link (external): 
https://drops.dagstuhl.de/opus/volltexte/2022/16093/pdf/LIPIcs-AofA-2022-7.pdf
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Research Areas: 
Mathematical and Algorithmic Foundations: 100%
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Science Branch: 
1020 - Informatik: 5%
1010 - Mathematik: 95%
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Appears in Collections:
Conference Paper

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