<div class="csl-bib-body">
<div class="csl-entry">Wallner, M. (2023, December 4). <i>Stretched exponentials and beyond</i> [Presentation]. Workshop: Computer Algebra for Functional Equations in Combinatorics and Physics 2023, Paris, France.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191543
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dc.description.abstract
The appearance of a stretched exponential term μⁿ^σ
with μ > 0 and σ ∈ (0,1) in a counting sequence cₙ)n≥0 is not common, although more and more examples are appearing lately. Proving that a sequence has a stretched exponential is often quite difficult. This is in part because such a sequence cannot be "very nice": its generating function cannot be algebraic, and it can only be D-finite if it has an irregular singularity.
Previously, the saddle-point method was the only generic method for proving such a phenomenon, but it requires detailed information about the generating function. Recently, together with Andrew Elvey Price and Wenjie Fang, we have developed a new method at the level of recurrences to prove stretched exponentials. I will introduce the basics of this method and show how it can be extended to other problems. Then I will summarize recent progress (new bijections, limit laws, etc.) in the study of compacted trees, a subclass of directed acyclic graphs. Finally, I will give an outlook on how these results now allow an in-depth study of limit shapes and open many new avenues for further research.
en
dc.language.iso
en
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dc.subject
Stretched exponentials
en
dc.subject
Asymptotics
en
dc.subject
Enumerative combinatorics
en
dc.subject
directed acyclic graphs
en
dc.subject
recurrence relations
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dc.title
Stretched exponentials and beyond
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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tuw.author.orcid
0000-0001-8581-449X
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tuw.event.name
Workshop: Computer Algebra for Functional Equations in Combinatorics and Physics 2023
en
tuw.event.startdate
04-12-2023
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tuw.event.enddate
08-12-2023
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tuw.event.online
Hybrid
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tuw.event.type
Event for scientific audience
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tuw.event.place
Paris
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tuw.event.country
FR
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tuw.event.institution
Institut Henri Poincaré
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tuw.event.presenter
Wallner, Michael
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tuw.event.track
Single Track
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.fulltext
no Fulltext
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item.grantfulltext
none
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item.languageiso639-1
en
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item.openairetype
conference presentation
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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crisitem.author.dept
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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crisitem.author.orcid
0000-0001-8581-449X
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie